Question

the ages and genders of people who attended a play are recorded below. what is the probability that a randomly selected male audience member is younger than 18?

age	female	male	total
18 – 34	45	30	75
35 – 49	78	72	150
50 and over	31	24	55
total	210	190	400

a $\frac{3}{10}$
b $\frac{32}{63}$
c $\frac{4}{21}$
d $\frac{32}{95}$

Explanation:

Step1: Determine the number of male audience members younger than 18

From the table, the number of male audience members 17 and under (younger than 18) is \(64\).

Step2: Determine the total number of male audience members

From the table, the total number of male audience members is \(190\).

Step3: Calculate the probability

The probability \(P\) that a randomly - selected male audience member is younger than 18 is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). So \(P = \frac{64}{190}=\frac{32}{95}\) (simplify the fraction \(\frac{64\div2}{190\div2}\)).

Answer:

D. \(\frac{32}{95}\)