The Motor Vehicle Department has found that the probability of a person pasing the test for a driver's license on the first try is 0.75. the probability that an individual who fails on the first ry will pass on the second try is 0.84, and the probability that an individual who fails the first and second test will pass the third time os 0.66 Find the probabilities that an individual will do the following.

a. P (fails both the first and second test) = b. P (Fail three times in a row) = c. P (Require at least two tries) =

a. 0.04

b. 0.0136

c. 0.2364

Step-by-step explanation:

a. P (fails both the first and second test)

=P (fails the first test) * P (fails second test)

= (1-P (pass on the first try)) * (1-P (fails on the first try will pass on the second try))

= (1-0.75) * (1-0.84) = 0.04

b. P (Fail three times in a row)

= P (fails both the first and second test) * P (fails third test)

=0.04 * (1-P (fails the first and second test will pass the third time))

=0.04 * (1-0.66) = 0.0136

c. P (Require at least two tries)

=P (fails on the first try will pass on the second try) + P (fails the first and second test will pass the third time)

= (P (fails the first test) * P (passes second test)) + (P (fails both the first and second test) * P (passes third test))

= (0.25 * 0.84) + (0.04 * 0.66)

= 0.2364