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.