Question

Amy entered her sister into their town's Smelly Shoe Competition. Amy observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes The probability that a contestant is 13 to 30 years old is 0.8, the probability that a contestant is wearing high heels is 0.7, and the probability that a contestant is 13 to 30 years old and is wearing high heels is 0.5. What is the probability that a randomly chosen contestant is 13 to 30 years old or is wearing high heels?

Answer 1

Given data:

the given probability that the contestant is 13 to 30 years old is P(A)=0.8.

The probability that the contestant wearing high heels is P(B)=0.7.

The probability that the contestant is 13 too 30 years old and wearing high heels is P(A ∩B)=0.5.

The expressionn for the probability that the contestant is 13 to 30 years old or wearing high heels is,

P(AUB)=P(A)+P(B)-P(A ∩B)

Substitute the given values in the above expression.

P(AU B)=0.8+0.7-0.5

=1

Thus, the probability that the contestant is 13 to 30 years old or wearing high heels is 1.