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

Answer:

(a)0.7

(b)0.42

Step-by-step 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.

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

(a)P(Female or under 10)

These are not mutually exclusive events, therefore:

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

(b) P(Under 10 or over 55)

These are mutually exclusive events, therefore:

$P (Under 10 or over 55)=P(Under 10)+P(Over 55)\\=\dfrac{11}{60}+ \dfrac{14}{60}\\=\dfrac{25}{60}\\\\=0.42$