Tennis Challenge In a recent U.S. Open tennis tournament, ther...

Question

Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.

d. If 1 of the 945 challenges is randomly selected, find the probability that it was made by a man or was upheld with an overturned call.

Accepted Answer

Hi everyone. Let's take a look at this practice problem. This problem says in a study analyzing quality checks at a fruit packaging facility, 945 fruits were randomly tested. Each fruit was either packaged by a manual or an automatic process and either passed or failed the quality check. The accompanying table lists the results. So, in our table, in the first row, we have manual pack packaging, and we have two columns. First column is past quality check, and it has a value of 175, and the second column is failed quality check, and that is 340. And the next row is automatic packaging, and under pass quality check, We have 120 and under failed quality check we have 310. If one fruit is randomly selected from the 945, what is the probability that it was packaged manually or pass the quality check? We're given four possible choices as our answers. For choice A, we have 0.055. For choice B, we have 0.468. For choice C, we have 0.791, and for choice D, we have 0.672. So we're asked to find the probability that our randomly selected fruit was either packaged manually or passed the quality check. And in order to do this, we're actually going to create two groups. We're gonna call Group A, the number of fruits that were packaged manually. That means that A, Is going to be equal to. 175. Plus 340. Which is equal to 515. And Group B is going to be those that pass the quality check. So, for Group B, that's going to be equal to, according to our table, 175 plus 120, which is going to be equal to 295. So, there are 515 fruits that were packaged manually, and 295 fruits that passed quality check. And what we're asked to do is to find the probability that the selected fruit is in A or B. So, since we're asked to find the probability that our fruit was in group A or B, we're going to use the general addition rule. So we call for the general edition rule that we have the probability of A or B, and that's going to be equal to the probability of A. Plus the probability of B. Minus The probability of A and B. And the reason why we want to subtract off the probability of A and B is cause we don't want to overcount. So we've already included in Group A, we don't want to count again when it shows up in Group B. So here we just need to determine each of those probabilities. And so for the probability of A, that is going to be equal to the probability of any quantity is going to be the number of favorable outcomes divided by the total number of outcomes. So the number of favorable outcomes is just the number of fruits that are in Group A, which is going to be 515, and this could be divided by the total number of fruits, which we're told the problem is 945. They don't have plus for the probability of B. The number of favorable outcomes is going to be 295. That's gonna be divided by the total number outcomes, which is 945 and then we'll have minus. For the probability of A and B, that's going to be the number of fruits that were packaged manually and passed quality check, and we can actually read that directly off of our table, and that is 175, and that's going to be divided by the total number of fruits, which is 945. And so we can evaluate this expression. Which is going to be equal to 0.672, and here we've just round it to three decimal places. So that is the answer that we're looking for for this problem. And if we compare that to our answer choices, we see that the correct answer choice corresponds to answer choice D. So I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Probability

Conditional Probability

Joint Probability

Watch next