Question

Elaine need to pass a certification exam. She has two tries to pass, otherwise she has to take the certification course again. On her first attempt, she has a 0.4 chance of passing. If she fails the first attempt, then she has a 0.6 chance of passing on her second attempt. The increase in the pass rate is due to her having a better idea of the kinds of test questions that are asked.

a) Draw a tree diagram to represent Elaine’s testing chances.

b) Use the random numbers below to simulate 5 repetitions of Elaine’s testing chances. Use these 5 repetitions to estimate the probability that Elaine passes the certification exam.

1st try: 1 -4 indicates Pass, 5 – 9, 0 indicates Fail

2nd try: 1 -6 indicates Pass, 7 – 9, 0 indicates Fail

15689 14227 84295

Answer 1

TREE DIAGRAM REPRESENTING ELAINE'S TESTING CHANCES:

Sl. No.	Random Numbers Drawn	Interpretation
1	1	Passed first exam
2	4	Passed first exam
3	2	Passed first exam
4	2	Passed first exam
5	7 , 8	Failed first exam(so another random number drawn) Failed second exam too

Clearly, in 5 repetitions of Elaine's testing chances, Elaine passed 4 times out of 5. Hence, the probability that Elaine passes the certification exam is: $\frac{4}{5}=0.80$