Question

# Elaine need to pass a certification exam. She has two tries to pass, otherwise she has...

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

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: $\frac{4}{5}=0.80$

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