Final answer:
The question involves calculating a binomial probability for exactly five out of ten U.S. adults to have very little confidence in newspapers. We use the binomial probability formula with n = 10 trials, k = 5 successes, and p = 0.68 as the probability of success on a single trial. The solution is found by computing the combination of 10 items taken 5 at a time, and then multiplying by the probabilities of success and failure raised to the appropriate powers.
Step-by-step explanation:
The question at hand involves calculating the probability of exactly five out of ten U.S. adults having very little confidence in newspapers, given that 68% of U.S. adults hold this view. This is a binomial probability problem where we want to find the probability of exactly 5 successes (adults with little confidence) out of 10 trials (the adults surveyed), with the probability of success on a single trial being 0.68. We 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 a single trial.
- k is the number of successes.
- n is the total number of trials.
Plugging the values into the formula, we get:
P(X = 5) = C(10, 5) * 0.68^5 * (1-0.68)^5
Calculating the combination C(10, 5) and then multiplying by the probabilities raised to their respective powers of successes and failures will give us the desired probability of this event occurring.