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.

Table showing tennis challenges: Men upheld 160, rejected 398; Women upheld 95, rejected 292.

e. If one of the challenges is randomly selected, find the probability that it was made by a man, given that the challenge was upheld with an overturned call.

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 study analyzing quality checks at a fruit packing facility, 945 fruits were randomly tested. Each fruit was either packed by a manual or an automatic process and either passed or failed the quality check. The accompanying table. It lists the results. So our column on the far right states failed quality check, and our column on the left states passed quality check. And for manual packaging, they passed the quality check was 175, and those who failed the quality check was 340. And for automatic packaging, those who passed the quality check was 120, and those who failed the quality check was 310. If one of the fruits is randomly selected and is known that the fruit passed the quality check, what is the probability that it was packed manually? Awesome. So it appears for this particular problem, we're trying to determine the probability that this particular fruit was packed manually if it passed the quality check. So with that said, now that we know that we're trying to find this specific probability value, let's read off our multiple choice answers to see what our final answer might be. A is 0.015, B is 0.593. C is 0.054 and D is 0.876. Awesome. So first off, let us know once again that we are asked to find the probability that a fruit was packed manually, given that it passed the quality check. So with that in mind, our first step to solve this particular problem is once again we need to completely and fully understand what we're being asked to solve for. So, we need to note that this particular problem is a conditional probability problem. So since because this is a conditional probability problem, we need to find the probability that a fruit was manually packed manually packed if we already know it past the quality check. So we're trying to find the probability of manual given. Past, which I'll use a capital M for manual and a capital P for past. So once again, we're trying to find the probability that the fruit was manually packed if we already know that it passed the quality check. So now, our second step is we need to recall and use the conditional probability formula, and the conditional probability formula states that the probability of a given B. Is equal to the probability of. A intersection B. Divided by P of B. Fantastic. So this upside down union symbol means intersection. So this is the intersection of sets. So that means that P of A intersection B, so the probability of A intersection B. Fantastic. And let us note that A denotes where the fruit was packed manually and B denotes where the fruit passed the quality check. So now our third step is we need to note that the probability that a intersection B, so this is the probability that the fruit was packed manually and passed, that would mean that the probability that A intersection B is equal to 175 divided by 945, and once again, we got this value of 175 from our table that is provided to us by the prom itself. So with that said, Our next step now. If we need to. Now we need to note that P of B, so now we're focusing our attention on P of B. So P of B is the probability that the fruit pass the quality check, and the probability that the fruit pass the quality check is going to be equal to 295 divided by 945, so 945. Awesome. Because we need to note that we have to add 175 plus 120 because that's how many fruit out of the 945 fruits that pass the quality check. So now our 4th and final step is we need to plug in all of our known variables back into our formula and solved, so the probability. Of M given P where M denotes manual and P denotes pasted. It's going to be equal to 175 divided by 945. Divided by 295 divided by 945. Which when we plug this into our calculator, you will find that it's approximately equal to when we round to three decimal places, 0.593, and that is our final answer. Hooray, we did it. And once again we had to note, we had, we have to note that we have to round to three decimal places because all of our multiple choice answers are rounded to three decimal places. So that will mean, without a doubt, our final answer is multiple choice answer letter B, which once again is 0.593. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Probability

Conditional Probability

Data Interpretation

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