Question

There are 24 male and 36 female patrons in a restaurant. Of the 11 patrons under 10 years old, 6 are male. Of the 14 patrons over 55 years old, 9 are female. A patron is selected at random. Find the probability. A. (Female or under 10) B. (Under 10 or over 55)

Answer 1

(a)0.7

(b)0.42

Explanation:

Definition: Mutually exclusive events are events that occur independently of one another.

The table below gives the distribution of the patrons in the restaurant.

`\left|\begin{array}c&$Male&$Female&$Total\\---&---&---&---\\$Under 10 years old&6&5&11\\10-55&13&22&35\\$Over 55 years old&5&9&14\\---&---&---&---\\$Total&24&36&60\end{array}\right|`

(a)P(Female or under 10)

These are not mutually exclusive events, therefore:

`P$(Female or under 10)=P(Female)+P(Under 10)-P(Female and Under 10)\\=(36)/(60)+ (11)/(60)-(5)/(60)\\=(42)/(60)\\\\=0.7`

(b) P(Under 10 or over 55)

These are mutually exclusive events, therefore:

`P$(Under 10 or over 55)=P(Under 10)+P(Over 55)\\=(11)/(60)+ (14)/(60)\\=(25)/(60)\\\\=0.42`