The same 15 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.
Number of Contestants by Score and Day
Day 1Day 2Day 3Total5 outof 513154 outof 5227113 outof 532382 outof 552181 outof 523160 outof 52327Total15151545
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 3 on Day 1 or Day 2, given that the contestant received a score of 3 on one of the three days?
We are looking for the following:
score of 3score of 3 on day 1 or 2
Since no contestant scored a score more than once, there are 8 contestants total who scored a score of 3.
Number of Contestants by Score and Day
Day 1Day 2Day 3Total5 outof 513154 outof 5227113 outof 532382 outof 552181 outof 523160 outof 52327Total15151545
score of 3score of 3 on day 1 or 2
=83+2
=85