Question

On the first try she has probability 0.2 of passing. If she fails on the first try, her probability on the second try increases to 0.3 because she learned something from her first attempt. If she fails on two attempts, the probability of passing on a third attempt is 0.4. She will stop as soon as she passes. The course rules force her to stop after three attempts in any case.
(a) Make a tree diagram of Elaine’s progress. Notice that she has different probabilities of passing on each successive try.
(b) Explain how to simulate one repetition of Elaine’s tries at the exam.

Answer 1

a. We clearly see by this tree- diagram that Elaine has different passing probabilities in each try.

b. To simulate one repetition of Elaine's try at the exam, we do the following-

Pick a random digit from 0 to 9 the following way

A single digit simulates one try, with

0 , 1 as PASS

2 , 3, 4, 5, 6, 7, 8, 9 as FAIL.

If PASS: Elaine passes and no need to continue

If FAIL: Do Trial 2

Trail 2 as:(Elaine's second attempt)

0 , 1, 2 as PASS

3, 4, 5, 6, 7, 8, 9 as FAIL.

If PASS: Elaine passes and no need to continue

If FAIL: Do Trial 3

Trail 3 as:(Elaine's third and final attempt)

0 , 1, 2, 3 as PASS

4, 5, 6, 7, 8, 9 as FAIL.