6. Three hundred viewers were asked if they were satisfied with TV coverage of a recent disaster

Question

6. Three hundred viewers were asked if they were satisfied with TV coverage of a recent disaster. (15 points) 

 

	Female (F)	Male (M)	TOTAL
Satisfied (S)	80	55
Not Satisfied (N)	120	45
TOTAL

 

If a viewer is to be randomly selected from those surveyed. 

 

1. Find the probability that the viewer is satisfied.  

 

 

 

 

 

1. Find the probability that the viewer is a female or the viewer is not satisfied. 

 

 

 

 

 

 

1. Find the probability that the viewer is satisfied given that the viewer is male.  

 

 

Answer 1

P(Satisfied) = (80 + 55)/300 = 135/300 = 0.45

The probability that the viewer is satisfied is 0.45.

P(Female or Not Satisfied) = P(Female) + P(Not Satisfied) - P(Female and Not Satisfied)

= 200/300 + 165/300 - 120/300

= (200 + 165 - 120)/300

= 245/300 ≈ 0.8167

The probability that the viewer is either a female or not satisfied is about 0.8167.

P(Satisfied | Male) = P(Male and Satisfied) / P(Male)

= (55/300) / (100/300)

= (55/300)*(300/100) = 55/100 = 0.55

The probability that the viewer is satisfied given that the viewer is a male is 0.55.