Question

39% of adults say cashews are their favonte kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut Find the probability that the number who say cashews are their favorte nut is (a) exacty three; (D) at least four, and (c) at most two. If convenient, use technology to find the probabilities.

Answer 1

Using a binomial probability calculator, the probability that the number who say cashews are their favorte nut is as follows:

a) Exactly three: P(3) = 0.1526

b) At least four: P(4) = 0.2195

c) At most two = 0.0946

The percentage or probability of adults who say cashews are their favorite kind of nut (p) = 39%

The number of randomly selected adults, n = 12

Applying the binomial probability formula:

`P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)`

Where:

n is the number of trials (in this case, 12 adults)

k is the number of successful outcomes (in this case, the number who say cashews are their favorite nut)

p is the probability of success (in this case, 39% or 0.39)

Using a calculator, the probability that the number who say cashews are their favorte nut is as follows:

a) Exactly three: P(3) = 0.1526

b) At least four: P(4) = 0.2195

c) At most two = 0.0946