According to insurance records a car with a certain protection system will be recovered 90% of the time. Find the probability that 5 of 6 stolen cars will be recovered.
The probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.9^5 * .1 = ?
To find the probability that 5 out of 6 stolen cars with a certain protection system will be recovered, we can use the binomial probability formula. The binomial probability formula is given by:
P(X = k) = (nCk) * p^k * q^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes.
n is the number of trials or stolen cars (in this case 6).
k is the number of desired successes (in this case 5).
p is the probability of success (in this case 0.9, since the car has a 90% chance of being recovered).
q is the probability of failure (1 - p, in this case 0.1, since the car has a 10% chance of not being recovered).
nCk (n choose k) is the number of ways to choose k successes from n trials, and it's calculated as: n! / (k! * (n-k)!)
Using these values in the formula, we can calculate the probability as follows:
P(X = 5) = (6C5) * (0.9^5) * (0.1^(6-5))
= (6! / (5! * (6-5)!)) * (0.9^5) * (0.1^1)
= 6 * 0.59049 * 0.1
= 0.354294
Therefore, the probability that 5 out of 6 stolen cars with the certain protection system will be recovered is approximately 0.3543.