Chapter 14, Problem 27E

a)

To determine

To find probability that all three responded “Protect the environment”.

Answer to Problem 27E

The probability that the all three responded “Protect the environment” is 0.1952

Explanation of Solution

Given:

  

Calculation:

The probability that the all three responded “Protect the environment”

  $=(\frac{583}{1005})\times (\frac{583}{1005})\times (\frac{583}{1005})=0.1952$

b)

To determine

To find probability that the none responded “Equally important”.

Answer to Problem 27E

The probability that thenone responded “Equally important” =0.9131

Explanation of Solution

Given:

  

Calculation:

The probability that the none responded “Equally important”

  $=(\frac{975}{1005})\times (\frac{975}{1005})\times (\frac{975}{1005})=0.9131$

c)

To determine

To explain the assumptions which need to compute probabilities.

Answer to Problem 27E

Independent responses.

Explanation of Solution

Given:

  

Calculation:

There should be independent responses to calculate the probabilities.

d)

To determine

To explain whether the assumption is reasonable.

Answer to Problem 27E

Yes.

Explanation of Solution

Given:

  

Calculation:

Yes, it is reasonable to assume that responses are independent since the three people were chosen at random.