Question

If Mrs. fields herself wants to verify that rate by beginning with a small sample of 10 randomly selected consumers, find the probability that exactly 9 of the 10 consumers recognize her brand name. Also, find the probability that the number who recognize her brand name is not nine.

Answer 1

The correct approach will be "0.612580".

Explanation:

Given:

Randomly selected customers,

n = 10

Probability of recognition,

p = 90%

or,

= 0.9

q = 1 - p

= 1 - 0.9

= 0.1

Now,

The probability that 9 out of 10 clients are likely to be familiar with the brand will be:

⇒
`P(X=r)=nCr* (p)^r* (q)^((n-r))`

⇒
`P(X=9)=10C_9* (0.9)^9* (0.1)^((10-9))`

`=10C_9* (0.9)^9* (0.1)^1`

`=10* (0.9)^9* 0.1`

`=0.387420`

hence,

The probability that not nine seem to be the numbers recognizing her brand name will be:

⇒
`P(X=not \ 9)=1-P(X=9)`

`=1-0.387420`

`=0.612580`