Question

According to a newspaper, 40% of bicycles stolen in a certain country are recovered. Find the probability that, in a sample of 5 randomly selected cases of bicycles stolen in the country, exactly 2 out of 5 bikes are recovered. The probability that exactly 2 out of 5 stolen bicycles are recovered is _________ (Type an integer or decimal rounded to three decimal places as needed.)

Answer 1

To find the probability that exactly 2 out of 5 stolen bicycles are recovered with a recovery rate of 40%, we use the binomial probability formula and get a result of approximately 0.346 after rounding to three decimal places.

Step-by-step explanation:

The student is asking about the probability of a specific outcome in a binomial distribution scenario, where there are only two possible outcomes for each trial - a bicycle is either recovered or not. To calculate the probability that exactly 2 out of 5 stolen bicycles are recovered, given that the recovery rate is 40%, we can use the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

Where:

X is the random variable representing the number of successes (bicycles recovered),

k is the number of successes (2 recovered bicycles),

n is the number of trials (5 stolen bicycles),

p is the probability of success on each trial (0.40, or 40%).

Plugging in the values:

P(X = 2) = (5 choose 2) * (0.40)^2 * (0.60)^3 = 10 * 0.16 * 0.216 = 0.3456

So, the probability that exactly 2 out of 5 stolen bicycles are recovered is 0.346 (rounded to three decimal places as required).