Using Probabilities for Significant Events

c....

Question

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. In a prize box game, each player opens 4 hidden compartments. The number of compartments that match a secret winning combination is recorded. Suppose that the probability of getting exactly 3 correct matches is 0.009. And that the probability of getting three or more correct matches is 0.010. Which of these probabilities should be used to decide whether getting three matches is unusually high, the probability of exactly 3 matches, or the probability of three or more matches. Awesome. So it appears for this particular problem, what we're ultimately trying to solve for is we're trying to determine which of these probabilities should be used to help us decide whether or not getting 3 matches is unusually high. Is it the probability of exactly 3 matches or the probability of 3 or more matches. So with that in mind, let's read off our multiple choice answers to see what our final answer might be. A is the probability of getting exactly 3 matches. B is the probability of getting 3 or more matches. C is none of these, D is both of these. Awesome. So, first off, let us write down all of our known information, all of our variables that are given to us. So let us note that we're told that the probability of getting exactly 3 matches is, and we'll call this P where P denotes the probability, so P of Exactly 3, which I'll just call E3, so the probability of getting exactly 3. Is equal to 0.009. And the probability of getting 3 or more matches, we'll call this 3 or more, so I'll call it 3 or M, so 3 or more is equal to 0.010, fantastic. So now we need to take a moment here to make sure we understand what the question is asking us to solve or what our problem is asking us to solve for. So let us recall and note that we want to determine whether getting 3 matches is significantly high result. In statistics, as we should recall, a result is often called significantly high if The probability of getting that result or something more extreme is very small. Typically 5% or less than. Meaning Less than or equal to 0.05. Fantastic. So that means our key concept that we have to keep in mind is, as we should recall and note, when evaluating whether a number of successes is significantly high, we use the probability of getting that number or more, not just the exact value. This is because we're interested in how rare or unusual it is to get at least that specific outcome. So with that in mind, we can now apply our concept. So with that in mind, if we use the probability of exactly 3 matches, which is 0.009 for the probability, We're only evaluating the chance of that specific outcome. But in order to judge how unusual it is to get 3 matches or more, we must consider all results that are as extreme or more extreme than 3 matches. So that includes either 3 matches. Or 4 matches. Fantastic, which is even more rare. So 4 matches is even more rare, so I'll put rare in quotation, sorry, rare in parentheses. So with that in mind, we need to recall and use that P of Capital X is greater than or equal to 3, will be equal to 0.010. So this gives us the complete picture of how unlikely it is to get 3 or more matches, so which is necessary for evaluating whether the outcome is considered significantly high. So that will mean our final answer without a doubt, will be that we should use the probability of getting three or more matches, which is 0.010. So that will mean, without a doubt, our final answer. Has to be multiple choice answer letter B, which once again is the probability of getting 3 or more matches. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Using Probabilities for Significant Events

c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?

Key Concepts

Probability Distribution

Significance Level

Comparative Analysis

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