binomial probabilities one in four adults is currently on a diet. Find the probability that the number who say they are currently on a dies is (a)exactly three, (b)at least three, and (c) more than three
To solve this problem, we can use the binomial probability formula. The formula for calculating the probability of x successes in n independent trials, where the probability of success is denoted by p, is given by:
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
In this case, the probability of success (p) is 1/4 since one in four adults is currently on a diet. We want to find the probability for different values of x: (a) exactly three, (b) at least three, and (c) more than three.
Let's calculate these probabilities one by one:
(a) Probability of exactly three adults on a diet:
To find this probability, we substitute x = 3, n = total number of adults, and p = 1/4 into the binomial probability formula.
P(3) = C(n, 3) * (1/4)^3 * (1 - 1/4)^(n - 3)
(b) Probability of at least three adults on a diet:
To find this probability, we need to sum up the probabilities for x = 3, 4, 5, ..., n.
P(at least 3) = P(3) + P(4) + P(5) + ... + P(n)
(c) Probability of more than three adults on a diet:
To find this probability, we need to subtract the probability of having three or fewer adults on a diet from the total probability of having adults on a diet.
P(more than 3) = 1 - P(at most 3) = 1 - (P(0) + P(1) + P(2) + P(3))
To calculate the probabilities in (a), (b), and (c), we need the total number of adults (n). If you provide the number of adults, I can assist you further and calculate the specific probabilities in this context.