Punnett Square Probability: Study with Video Lessons, Practice Problems & Examples

Understanding Punnett squares involves applying the rule of multiplication and the rule of addition to calculate probabilities of genetic outcomes. The multiplication rule, or and rule, states that the probability of two independent events occurring together is found by multiplying their individual probabilities. Conversely, the addition rule, or or rule, involves adding the probabilities of mutually exclusive events. For example, the probability of two coins landing on heads or tails can be calculated using these rules, enhancing comprehension of genetic inheritance patterns.

Punnett Square Probability

In this video, we're going to begin our lesson on Punnett Square probability or probabilities that relate to Punnett squares. Now, throughout this lesson, we're going to relate the probability of coin flips to the probabilities of Punnett squares. The reason that we can relate the probability of coin flips to the probabilities of Punnett squares is that they are representing independent events. Two events are independent of one another if the outcome of one event does not affect the outcome of the other event. For example, the outcome of one coin flip does not impact or affect the outcome of a second coin flip. Just like the outcome of one fertilization event does not impact or affect the outcome of another fertilization event. And so that's why, again, the probability of coin flips can be related to the probabilities of Punnett squares. Now, moving forward throughout this lesson, we're going to introduce and explain two different rules when it comes to the probabilities of Punnett squares. The first rule is going to be the rule of multiplication, whereas the second rule that we're going to introduce is the rule of addition. The rule of multiplication or the rule of addition can be used to determine probabilities and to predict genetic crosses. Again, we'll explain and introduce these rules as we move forward in our course in their own separate videos. But for now, notice down below what we're showing you are independent events of these two coin flips. And so notice over here, we're showing you coin flip number 1, and coin flip number 1 has a 50% probability of landing on heads and another 50% probability of landing on tails. And so again, 50% is the same as one half. And then over here, what we're showing you is coin flip number 2, and coin flip number 2 is an independent event from coin flip number 1 because the outcome of coin flip number 1 does not impact or affect the outcome of coin flip number 2. And so when we flip coin number 2, there's still a 50% probability that it will land on heads and a 50% probability that it will land on tails. And so you can imagine that these coins here represent alleles, and so when you do that, you can use the coins to generate a Punnett square, as we can see here. And so you can see, this square here is representing the possibility of both coins landing on heads. This one is representing the possibility of one landing on heads, one landing on tails. This one's the probability of landing one on tails, one on heads. And this one's the probability of both of them landing on tails. And so again, we are going to be relating the probability of coin flips to the probabilities of Punnett squares as we move along through this lesson. And so this here concludes our introduction to Punnett square probabilities. And again, in our next lesson video, we're going to introduce and explain the rule of multiplication. So I'll see you all in that video.

Rule of Multiplication (the AND Rule)

In this video, we're going to introduce the rule of multiplication, which is also sometimes called the and rule. The rule of multiplication, as its name implies, involves multiplication. It is also sometimes referred to as the product rule or the and rule. We'll explain why it's called the and rule shortly later in this video. The reason it is known as the product rule is that the product is the answer to a multiplication problem. Hence, by saying the product rule, it's implied that multiplication is involved. The rule of multiplication, the product rule, and the and rule all refer to the same concept. They essentially state that the probability for multiple independent events is computed by multiplying the probabilities of individual events where the conditions are met.

For example, the probability that two coins, coin number 1 and coin number 2, both land on tails requires taking the probability of one coin landing on tails alone and multiplying it by the probability of the other coin landing on tails alone. When we do this multiplication, we obtain: 1 2 × 1 2 = 1 4 .

This rule of multiplication is called the and rule because the word "and" is usually used to refer to two events occurring together, such as coin 1 and coin 2 both landing on tails. If we take a look at our image here on the left-hand side, it shows the probability of flipping two coins at once. If we flip the first coin, there's a 50% chance of landing on heads and a 50% chance of landing on tails, represented as 1/2 probability of landing on tails. However, we're focusing on the probability that both coins land on tails. Each coin flip is a completely independent event. So there's still a 50% chance that coin number 2 will land on tails. We need to implement the rule of multiplication to find the probability that both coins will land on tails together. Thus, the probability that these two coins will both land on tails is: 1 2 × 1 2 = 1 4 .

On the right-hand side, we show another application of the multiplication rule by looking at heterozygous parental pea plants with two offspring. What is the probability they will both be green? Since one fertilization event is independent from another, when considering two offspring, we are really discussing two fertilization events that are independent. In this example, the probability that one offspring will be green is 1 out of 4 total possibilities, or 1/4. Hence, the probability that both offspring will be green is: 1 4 × 1 4 = 1 16 . This computation gives us the answer to this example problem, thus concluding our introduction to the rule of multiplication, the product rule, and the and rule. We'll practice applying these concepts as we move forward in our course, and then we'll discuss the rule of addition. I'll see you in our next video.

Calculate the probability of 2 heterozygous (Rr) parents having 3 homozygous recessive (rr) offspring.

• A. 1/32.
• B. 1/16.
• C. 3/16.
• D. 1/64.
• E. 3/4.

Rule of Addition (the OR Rule)

So now that we've covered the rule of multiplication in our previous lesson video, in this video we're going to introduce the rule of addition, which is also sometimes referred to as the or rule. Now the rule of addition, as its name implies, is going to involve addition, and the rule of addition is also sometimes called the sum rule or the or rule. Now again, we'll explain why it's called the or rule a little bit later here in this video. But the reason it's called the sum rule is because the sum is the answer to an addition problem, and so the sum is implying addition. Now the rule of addition, the sum rule, and the or rule are all referring to the same thing. And really what they say is that the probability that one independent event or another independent event will occur is calculated by adding their probabilities. And so this is another reason why it's called the or rule. It's because it's involving the probability of one event or another event. And so for example, the probability that 2 coins will both land on heads or both land on tails is going to be the probability of one event plus the probability of another event. So the probability that they both land on heads is 14 and the probability that they both land on tails is 14, and so the probability that one or the other will occur is 14 plus 14. And 14 plus 14 is of course 24, And 24 is the same exact thing as 12. And so there's a 50% chance of 2 coins landing on heads or 2 coins landing on tails. And so if we take a look at our image down below over here on the left hand side, we can get a better understanding of that example with the coins. And again, we know that the first coin flip has a 50% probability of landing on tails, 50% probability of landing on heads. And the second coin flip has a 50% probability of landing on heads and a 50% probability of landing on tails since they are the probability of 1 coin landing on heads and multiply it by the probability of another coin landing on heads. And so 1 half times 1 half is 14, and so the probability that both coins will land on heads is 14 probability. And the same goes for both coins landing on tails. The probability of 1 coin landing on tails is 1 half. The probability of another coin landing on tails is 1 half. And so the probability that both of these coins will land on tails together is 1 half times 1 half which is 14. And so the probability that they both will land on heads is 14. The probability that they will both land on tails is 14. However, to get the probability that the coins will land both on heads or both on tails, we need to take the probability of these occurring independently and add them together. And so the probability of both of them landing on heads is 14, and the probability of both of them landing on tails is 14. And so if we want the probability of them landing on heads or landing on tails, then we add them together. And so notice the addition sign here. And 14 plus 14 is again 24, which is the same thing as 12. And so there's a 1 half probability of them both, of them landing on, of them both landing on heads or both landing on tails. Now over here on the right, what we're showing you is another application of the addition rule as it applies to this particular probability of having a homozygous dominant or a homozygous recessive offspring. And so of course when we take a look at this Punnett square, the probability of getting a homozygous dominant offspring is 14, and the probability of getting a homozygous recessive offspring is also 14. However, to get the probability of getting a homozygous dominant or homozygous recessive, we need to add these probabilities together. And so the probability that the offspring is dominant is 14. The probability that the offspring is homozygous recessive is 14, and if we want the probability that one event or the other event will occur, we need to add them, and that's again while we have the addition sign here and so 14 plus 14 is 24, which is the same thing as 12. So there's a one half probability or a 50% recessive.

This here concludes our introduction to the rule of addition or the sum rule or the or rule. And we'll be able to get some practice applying these concepts as we move forward in our course. So I'll see you all in our next video.

What is the probability that a plant from a monohybrid cross of heterozygous parents, is homozygous dominant OR homozygous recessive?

• A. ½.
• B. ¼.
• C. ¾.
• D. 1.

A blue-eyed female that is homozygous recessive and a brown-eyed male that is heterozygous mate, producing two offspring. What is the probability that one child will have blue eyes AND one will have brown eyes? (Eye color is controlled by a single gene).

• A. ½.
• B. ¼.
• C. ¾.
• D. 1.

A homozygous dominant male has a child with a heterozygous female. What is the probability that the child will have the same genotype as its father OR its mother?

• A. ½.
• B. ¼.
• C. ¾.
• D. 1.

Here’s what students ask on this topic:

What is the rule of multiplication in Punnett square probability?

The rule of multiplication, also known as the 'and rule' or the 'product rule,' is used to determine the probability of two or more independent events occurring together. In the context of Punnett squares, it involves multiplying the probabilities of individual genetic outcomes. For example, if the probability of one allele being passed on is 1/2 and the probability of another independent allele being passed on is also 1/2, the combined probability of both events occurring is 1/2 × 1/2 = 1/4. This rule is essential for predicting the likelihood of specific genotypes in offspring.

How does the rule of addition apply to Punnett square probability?

The rule of addition, also known as the 'or rule' or the 'sum rule,' is used to calculate the probability of either of two independent events occurring. In Punnett squares, this involves adding the probabilities of different genetic outcomes. For instance, if the probability of obtaining a homozygous dominant genotype is 1/4 and the probability of obtaining a homozygous recessive genotype is also 1/4, the combined probability of either event occurring is 1/4 + 1/4 = 1/2. This rule helps in determining the overall likelihood of various genetic combinations in offspring.

How can coin flips be related to Punnett square probabilities?

Coin flips can be related to Punnett square probabilities because both represent independent events. In a coin flip, the outcome of one flip does not affect the outcome of another. Similarly, in genetic crosses, the outcome of one fertilization event does not impact another. For example, the probability of flipping two heads in a row is 1/2 × 1/2 = 1/4, similar to the probability of inheriting two specific alleles. This analogy helps in understanding the application of the multiplication and addition rules in Punnett squares.

What is the probability of two heterozygous pea plants producing a green offspring?

To determine the probability of two heterozygous pea plants (Gg) producing a green offspring, we need to consider the Punnett square. The possible genotypes are GG, Gg, Gg, and gg. Green offspring are represented by the gg genotype. The probability of obtaining gg is 1/4. Therefore, the probability of two heterozygous pea plants producing a green offspring is 1/4 or 25%.

How do you calculate the probability of multiple offspring having the same genotype using the rule of multiplication?

To calculate the probability of multiple offspring having the same genotype, you use the rule of multiplication. For example, if the probability of one offspring being homozygous recessive (gg) is 1/4, and you want to find the probability of two offspring both being gg, you multiply the individual probabilities: 1/4 × 1/4 = 1/16. This means there is a 1/16 probability that both offspring will have the homozygous recessive genotype.