In a region, there is a 0.7 probability chance that a randomly selected person o

Question

In a region, there is a

0.7

probability chance that a randomly selected person of the population has brown eyes. Assume

13

people are randomly selected. Complete parts (a) through (d) below.

a. Find the probability that all of the selected people have brown eyes.

The

probability that all of the

13

selected people have brown eyes is

(Round to three decimal places as needed.)

b. Find the probability that exactly

12

of the selected people have brown eyes.

The

probability that exactly

12

of the selected people have brown eyes is

(Round to three decimal places as needed.)

c. Find the probability that the number of selected people that have brown eyes is

11

or more.The probability that the number of selected people that have brown eyes is

11

or more is

(Round to three decimal places as needed.)

Explanation / Answer

PROBABILITY OF HAVING BROWN EYES = 0.7

PROBABILITY OF NOT HAVING BROWN EYES = 1 - 0.7 = 0.3

A) 13 SELECTED AND ALL HAVE BROWN EYES = 13C13*(0.7)^13(0.3)^0 = 0.0096

B) OUT OF 13 12 HAVE BROWN = 13C12*(0.7)^12*(0.3)^1 = 0.053

C)11 OR MORE PEOPLE HAVING BROWN EYES = 11 PEOPLE + 12 PEOPLE + 13 PEOPLE

= 13C11*(0.7)^11*(0.3)^2 + PROBABILITY IN PART A + PROBABILITY IN PART C = 0.138 + 0.053+ 0.0096 =0.2014

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