Assume that when adults with smartphones are randomly selected, $49 \%$ use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes.
The probability is (Round to four decimal places as needed.)
Answer
Final Answer: The probability that exactly 4 out of 8 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately \(\boxed{0.2730}\).
Step 1 ：Define the problem as a binomial probability problem, where 'n' is the number of trials (8 adult smartphone users), 'p' is the probability of success (0.49, the probability that an adult uses their smartphone in meetings or classes), and we are asked to find the probability of 'k' successes (4 adults using their smartphones in meetings or classes).
Step 2 ：Use the formula for binomial probability: \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\), where \(C(n, k)\) is the combination of n items taken k at a time, \(p\) is the probability of success, and \((1-p)\) is the probability of failure.
Step 3 ：Calculate the combination \(C(n, k)\) as 70.
Step 4 ：Calculate \(p^k\) as 0.05764800999999999.
Step 5 ：Calculate \((1-p)^(n-k)\) as 0.06765201.
Step 6 ：Calculate the final probability as \(P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k)) = 70 * 0.05764800999999999 * 0.06765201 = 0.2730002624300069\).
Step 7 ：Final Answer: The probability that exactly 4 out of 8 randomly selected adult smartphone users use their smartphones in meetings or classes is approximately \(\boxed{0.2730}\).
