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Probability and conditional probability SAT question
Math · Problem-Solving and Data Analysis · Hard · Answer it here, explanation included.
| 5 out of 5 | 4 out of 5 | 3 out of 5 | 2 out of 5 | 1 out of 5 | 0 out of 5 | Total | |
|---|---|---|---|---|---|---|---|
| Day 1 | 2 | 3 | 4 | 6 | 2 | 3 | 20 |
| Day 2 | 2 | 3 | 5 | 5 | 4 | 1 | 20 |
| Day 3 | 3 | 3 | 4 | 5 | 3 | 2 | 20 |
| Total | 7 | 9 | 13 | 16 | 9 | 6 | 60 |
The same 20 contestants, on each of 3 days, answered 5 questions in order to win a prize. Each contestant received 1 point for each correct answer. The number of contestants receiving a given score on each day is shown in the table above.
No contestant received the same score on two different days. If a contestant is selected at random, what is the probability that the selected contestant received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days?
Enter a number or fraction (like 3/17 or 0.176). Press Enter to check.
ExplanationShow
The correct answer is 
. It is given that no contestant received the same score on two different days, so each of the contestants who received a score of 5 is represented in the “5 out of 5” column of the table exactly once. Therefore, the probability of selecting a contestant who received a score of 5 on Day 2 or Day 3, given that the contestant received a score of 5 on one of the three days, is found by dividing the total number of contestants who received a score of 5 on Day 2 or Day 3 
by the total number of contestants who received a score of 5, which is given in the table as 7. So the probability is . Note that 5/7, .7142, .7143, and 0.714 are examples of ways to enter a correct answer.
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