The probability of recovering exactly 5 cars is given by the following formula:
P(X = k) = nCk * p^k * (1 - p)^(n-k)
where:
k is the number of successes (in this case, the number of cars recovered)
n is the total number of trials (in this case, the total number of stolen cars)
p is the probability of success on each trial (in this case, the probability of recovering a car)
Therefore, the probability of recovering exactly 5 cars is:
P(X = 5) = 7C5 * 0.85^5 * 0.15^2
= 21 * 0.411641 * 0.0225
= 0.192542
Therefore, the probability of recovering 5 out of 7 stolen cars is approximately 0.1925.
