Question

In a survey of 3000 Americans aged 12 through 74 years, the following makeup of the moviegoer audience was obtained.

Age	12–24	25–44	45–64	65–74
Audience (%)	30	32	24	14

A moviegoer is selected at random from the respondents of the survey.

(a) What is the probability he or she is between 12 and 24 years of age?


(b) What is the probability he or she is between 25 and 64 years of age?


(c) What is the probability he or she is between 12 and 24 years of age or between 65 and 74 years of age?

Answer 1

Total number of audience = 30 +32 +24 + 14 = 100

a) Probability that he or she is between 12 and 24 years of age

= 30 / 100

= 0.3

Probability that he or she is between 12 and 24 years of age is 0.

b)

probability he or she is between 25 and 64 years of age

= probability he or she is between 25 to 44 years of age * probability he or she is between 45 to 64 years of age

= (32/100) * (24 /100)

= 0.32 * 0.24

= 0.0768

Probability he or she is between 25 and 64 years of age is 0.0768

c)

probability he or she is between 12 and 24 years of age or between 65 and 74 years of age

= probability he or she is between 12 to 24 years of age + probability he or she is between 65 to 74 years of age

= (30/100)++ (14/100)

= 0.30 + 0.14

= 0.44

Probability he or she is between 12 and 24 years of age or between 65 and 74 years of age is 0.44