Question

When Allen takes a driving test, he has a probability of 0.21 of passing. i) Find the probability that Allan takes the test more than 6 times in order to pass. ii) What is the expected number of tests Allan will have to take in order to pass?

Answer 1

To find the probability that Allan takes the test more than 6 times in order to pass, calculate the probability of failing the test in the first 6 attempts. The probability that Allan takes the test more than 6 times is 0.181. The expected number of tests Allan will have to take to pass is approximately 4.8.

Step-by-step explanation:

i) Find the probability that Allan takes the test more than 6 times in order to pass:

To find the probability that Allan takes the test more than 6 times in order to pass, we need to find the probability of failing the test in the first 6 attempts. Since Allan has a probability of 0.21 of passing the test, the probability of failing is 1 - 0.21 = 0.79.

So, the probability that Allan takes the test more than 6 times is (0.79)6 = 0.181 or 18.1%.

ii) What is the expected number of tests Allan will have to take in order to pass:

The expected number of tests Allan will have to take in order to pass is the reciprocal of the probability of passing the test in one attempt.

So, the expected number of tests is 1/0.21 = 4.76 or approximately 4.8 tests.