Answer to Question #185421 in Statistics and Probability for maryam

Question

in a group of 20 adults, 4 out of 7 women and 2 out of the 13 men wear glasses. What is the probability that a person chosen at random from the group is a woman or someone who wear glasses? 

Answer 1

There are 7 women in the group and 13 men. 6 people wear glasses whereas 13 does not. There are 4 women who wear glasses.

Let A be the event that one is a woman and B be the event that they wear glasses.

probability that one is a female or wears glasses$P(A\cup B)$

$P(A \cup B)= P(A)+P(B)-P(A \cap B)$

$=\frac 7 {20}+\frac 6 {20}-\frac 4 {20}$

$=\frac 9 {20}$