Answer :
The binomial probability problem, requiring the use of the binomial probability formula to calculate the chance of exactly 5 out of 8 voters supporting the incumbent given a 42% support rate.
The probability of a specific outcome in a binomial experiment. Here, we need to use the binomial probability formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where:
- C(n, k) is the combination of n items taken k at a time
- p is the probability of success on any given trial (42% or 0.42 in this case)
- k is the number of successes (5 voters supporting the incumbent)
- n is the total number of trials (8 voters selected)
By applying the formula, we can calculate the probability that exactly 5 out of 8 randomly selected voters will support the incumbent when the support is at 42% overall.