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 below. 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 4 out of 5 on Day 1 or Day 3, given that the contestant received a score of 4 out of 5 on one of the three days?
Number of Contestants by Score and Day
| 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 |
