a survey from a research firm found that 30% of teenage consumers receive their spending money from part-time job.if five teenagers are selected at random,find the probability that only three of them will have part-time jobs.

To find the probability that only three out of five selected teenagers will have part-time jobs, we can use the binomial probability formula. The formula is given by:

P(X = k) = (n C k) * 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 on a single trial (given as 30% or 0.3 in this case), and
- (n C k) is the binomial coefficient, calculated as n! / (k! * (n-k)!)

In this case, we want to find the probability of exactly three teenagers having part-time jobs, so we plug in the values:
n = 5 (number of teenagers selected),
k = 3 (number of successes),
p = 0.30 (probability of each teenager having a part-time job).

Let's calculate it step by step:

Step 1: Calculate the binomial coefficient
(n C k) = (5 C 3) = 5! / (3! * (5 - 3)!) = 5! / (3! * 2!) = (5 * 4) / (2 * 1) = 10

Step 2: Calculate the probability
P(X = 3) = (n C k) * p^k * (1 - p)^(n - k)
= 10 * (0.30^3) * (1 - 0.30)^(5 - 3)
= 10 * 0.027 * 0.49
= 0.1323

Therefore, the probability that exactly three out of five selected teenagers will have part-time jobs is approximately 0.1323, or 13.23%.

The easiest way to do this problem is to use a binomial probability table. Your values to look up in the table would be the following:

n = 5, p = .3, and x = 3

I hope this will help.