COMPLETELY CONFUSED

Question

A brand name has a 60% recognition rate. Assume the owner of the brand wants to verify that rate by beginning with a small sample of 7 randomly selected consumers. Complete parts (a) through (d) below.

a. What is the probability that exactly 6 of the selected consumers recognize the brand name?

The probability that exactly 6 of the 7 consumers recognize the brand name is ?

Answer 1

This is a Binomial distribution of Bernoulli trials.

probability of success p = 0.6

probability of no success  q = 1- 0.6 = 0.4

Number of trials  n = 7

Number of success r = 6

 

Probability of 6 successes in 7 trials = nCr . p^r . q ^ (n-r)

Substitute and solve.

Answer 2

This is a basic Binomial probability with p=0.6 and q=0.4

 

The formula is   ₇C₆·0.6⁶·0.4¹ = 0.1306368