Question

98 points- Math help, PROBABILITY
For the members of a neighborhood meeting group, the probability of randomly selecting a member who likes to cook is 42%, the probability of randomly selecting a member who likes to sew is 23%, and the probability of randomly selecting a member who likes to both cook and sew is 7%.

What is the probability of randomly selecting a member who likes to cook or likes to sew?

Answer 1

For two events A and B,

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

We're given all of the probabilities on the right hand side:

$P(\text{cook OR sew})=P(\text{cook})+P(\text{sew})-P(\text{cook AND sew})$

$\implies P(\text{cook OR sew})=42\%+23\%-7\%=58\%$

Answer 2

The keyword here is "or", this means it wants the probability of finding a person who likes to cook -- or a person who likes to sew.

We are given both of these probabilities, and to find the probability of finding someone who likes to do activity A OR activity B, we simply add the probability of activity A and activity B.

42 + 23 = 65% of members like to cook or like to sew.