Lost Luggage in Airlines Transportation

officials reported that 8.25 out of every 1000 airline
passengers lost luggage during their travels last year. If
we randomly select 400 airline passengers, what is the
probability that 5 lost some luggage?

=0.1203

To find the probability that exactly 5 out of 400 airline passengers lost some luggage, we need to use the binomial probability formula. The binomial probability formula is:

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

Where:
- P(X=k) is the probability of exactly k successes,
- n is the number of trials,
- k is the number of successes,
- p is the probability of success in one trial, and
- (nCk), or "n choose k," represents the number of ways to choose k items from a set of n items.

In this case:
- n = 400 (the number of airline passengers)
- k = 5 (the number of passengers who lost luggage)
- p = 8.25/1000 (the probability of a passenger losing luggage)

Let's calculate the probability using the formula:

P(X=5) = (400C5) * (8.25/1000)^5 * (1-8.25/1000)^(400-5)

To calculate (400C5), we need to use the formula for combinations:

(400C5) = 400! / (5! * (400-5)!)

After calculating, the final result will be the probability that exactly 5 passengers out of 400 lost their luggage.