Certainly! To find the probability that exactly 10 out of the 50 executives say that older workers have blocked their career advancement, we can use the binomial probability formula. This is because the problem you described is a binomial experiment - there are a fixed number of trials (n=50), each trial has only two possible outcomes (either an executive says older workers have blocked their career advancement or not), the probability of success (saying older workers have blocked their career advancement) is constant (p=0.24), and the trials are independent.
The binomial probability formula is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k),
where:
- P(X = k) is the probability of having exactly k successes in n trials.
- n is the number of trials (in this case, 50).
- k is the number of successes (in this case, 10).
- p is the probability of success on a single trial (in this case, 0.24).
- (n choose k) is the number of ways to choose k successes out of n trials and is calculated as n! / (k! * (n-k)!), where "!" denotes the factorial function.
Plugging in the values:
P(X = 10) = (50 choose 10) * 0.24^10 * (1-0.24)^(50-10)
= (50! / (10! * (50-10)!)) * 0.24^10 * (1-0.24)^(50-10)
≈ 0.054.
This means there's approximately a 5.4% chance that if you randomly select 50 executives, exactly 10 of them will say that older workers have blocked their career advancement.