Probability of distribution

Question

46% of adults say cashews are their favorite 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 says cashews are their favorite nut is( A) exactly 3 (B) at least 4 (c) at most 2. If convenient, use technology to find the probabilities

Answer 1

use the binomial formula to find the probabilities. n = number of trials (12), p = probability of success (0.46) and x = number of successes:

probability of x successes in 12 tries with probability of success = 0.46

12!

------ 0.46^x * 0.54^12-x

x! (12-x!)

for part a) x = 3

for part b) find probabilities for x= 0, 1, 2 and 3, sum those probabilities and subtract from 1

for part c) find probabilities for x = 0, 1 and 2 and sum those probabiities