Question 2 7marks Miss Piggy has three attempts to pass her driving test. She is
ID: 3059821 • Letter: Q
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Question 2 7marks Miss Piggy has three attempts to pass her driving test. She is enthusiastic neither about driving nor preparing, so the probability of her passing the test on the first attempt is 0.6 We know that if she fails on the first attempt, she starts practising hard and increases her success probability up to 0.75 before the second attempt. If she fails again, she improves further to achieve the probability of 0.9 to pass the test before the third attempt. (a) What is the probability that Miss Piggy will pass the test? b) What is the probability that she will pass the test and do so on the third attempt?Explanation / Answer
Total attempts = 3
Given information
probability of passing the test on first attempt = 0.6
probability of success on second attempt = 0.75
probability of success on third attempt = 0.9
PART (a)
Probability that miss piggy will pass the test?
Miss Piggy has 3 possible cases to pass the test:
case 1.Miss Piggy passes her driving test in the first attempt
case 2.She fails in the first attempt and works hard and passes the driving test on the second attempt.
case 3.She fails in the first two attempts and works harder and passes on the third attempt.
therefore,
total probability of Miss Piggy passing the driving test = probability of case 1 + probability of case 2 + probability of case 3
probability of case 1 = 0.6
probability of case 2 = (probability of failing the test on first attempt)*(probability of success on the second attempt)
since probability of success on first attempt = 0.6
therefore, probability of failure on first attempt = 1-probability of success on first attempt = 1-0.6 = 0.4
therfore,
probability of case 2 = 0.4*0.75 = 0.3
probability of case 3 = (probability of failing the test on first attempt)*(probability of failing on the second attempt)*(probability of success on the third attempt)
since probability of success on second attempt = 0.75
therefore, probability of failure on second attempt = 1-probability of success on second attempt
= 1-0.75 = 0.25
we have already calculated
probability of failure on first attempt = 0.4
therfore,
probability of case 3 = 0.4*0.25*0.9 = 0.09
therefore,
total probability of Miss Piggy passing the driving test = 0.6 + 0.3 + 0.09 = 0.99
PART (b)
probability that she will pass the test and do so on third attempt?
this means that she fails on the first and the second attempt, works hard and passes the test on the third attempt
the required probability = (probability of failure on the first attempt)*(probability of failure on the second attempt)*(probability of success on the third attempt)
[ probability of failure on the first attempt = 1-probability of success on the first attempt = 1-0.6 = 0.4
probability of failure on the second attempt=1-probability of success on the success attempt=1-0.75 =0.25
probability of success in the third attempt = 0.9 ]
therefore,
the required probability = 0.4*0.25*0.9 = 0.09
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