For a single dice roll, there is a 1/6 chance that any p...

Question

For a single dice roll, there is a 1/6 chance that any particular number will appear. For a pair of dice, each specific combination of numbers has a probability of 1/36 occurring. Most total values of two dice can occur more than one way. As a test of random probability theory, a student decides to roll a pair of six-sided dice 300 times and tabulate the results. She tabulates the number of times each different total value of the two dice occurs. Her results are the following:

Total Value of Two Dice Number of Times Rolled
2 7
3 11
4 23
5 36
6 42
7 53
8 40
9 38
10 30
11 12
12 8
TOTAL 300

The student tells you that her results fail to prove that random chance is the explanation for the outcome of this experiment. Is she correct or incorrect? Support your answer.

Accepted Answer

Welcome back. Let's look at our next problem. It says probability is a measure of the likelihood of an event occurring which the following statements is false about probability. So we'll look at our answer choices and evaluate them. I'm noticing as we glance over them all, it's asking about probabilities being one or zero and we finish up with toys d being none of these. So we want to keep in mind that there's a possibility that none of the answers will be false. So before we evaluate our answer choices, let's just think briefly about the mathematical meaning of probability since we have numbers and our answer choices and that would be the number of desired or favorable outcomes divided by the total number of possible outcomes. So if we did an example, we talk about a coin toss maybe really basic example, the total number of desired outcomes, we will say, what's the probability will get heads? The probability of coin toss equaling heads. Well, what are the number of desired outcomes? Just one Heads turning up when we flip our coin? What are the total number of possible outcomes to we can get heads or tails? So one divided by 21 half or 50%. So just using that really basic example to help us think about what is the mathematical or numerical meaning of a probability. So with that in mind, let's look at our answer choices. Choice A is if the probability of an event is one then it is certain an event will occur. So let's think about what one means if that's the equal, if that's the outcome of our probability equation. So that would mean that the number of desired outcomes is the same as the total number of possible outcomes. That would mean the event will always occur. Our desired outcome is the same as the number of possible outcomes. There are no other outcomes other than the one we're interested in. So this is a true statement which means that it cannot be our answer. So we eliminate answer choice. A Joyce D says none of these, meaning none of these are false. Well, we already have one false answer so we can eliminate choice D. Now let's look at choice B. Choice B says if the probability of an event is zero, then the event can't occur. Well, again, if we think of our formula for probability, if an event is zero, we can't have zero as the denominator. That's an undefined, gives us an undefined result. So that would mean zero must be in the numerator. That would mean the number of desired outcomes or the outcome we're interested in will occur zero times. So this is a true statement. If the probability is zero, that means the event will not occur. It's a true statement. So choice B is not our answer. So now we're left with choice C, the probability of an event can be greater than one or less than zero. Well, we kind of know by process of elimination, this is the one that's false. But let's look at that more carefully. We know that an event, probability event being one means it is certainly event will occur to have a probability be greater than one. That would mean our outcome, our desired outcome occurs more times than possible. So that is meaningless. So it cannot be greater than one. It also cannot be less than zero, zero means it won't occur. So probability must be in between zero and one. So choice C will then be our correct answer. Which of the following statements is false about probability choice. See the probability of an event can be greater than one or less than zero. See you in the next video.

Key Concepts

Probability Theory

Randomness and Variability

Statistical Significance

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