Answer: To find the probability of each event, we can use the binomial probability formula:
P(x) = (nCx) * p^x * (1 - p)^(n - x)
where:
P(x) = Probability of getting exactly x successes
n = Total number of trials (in this case, 10 U.S. adults)
x = Number of successes we want to find the probability for
p = Probability of success in a single trial (in this case, 0.61, since 61% have very little confidence in newspapers)
(1 - p) = Probability of failure in a single trial (1 - 0.61 = 0.39)
(a) To find the probability of exactly five U.S. adults having very little confidence in newspapers:
P(5) = (10C5) * 0.61^5 * 0.39^(10 - 5)
Using the combination formula, (nCx) = n! / (x!(n-x)!):
P(5) = (10! / (5!(10-5)!)) * 0.61^5 * 0.39^5
P(5) = (10! / (5! * 5!)) * 0.61^5 * 0.39^5
P(5) = (10 * 9 * 8 * 7 * 6 / (5 * 4 * 3 * 2 * 1)) * 0.61^5 * 0.39^5
P(5) = (30,240) * 0.61^5 * 0.39^5
P(5) ≈ 0.146 (rounded to three decimal places)
So, the probability of exactly five U.S. adults having very little confidence in newspapers is approximately 0.146 (or 14.6%).