SOLUTION: The probability that Olivia will have to wait before she can cross Westgate Street is 1/3 and the probability that she will be able to cross high street without waiting is 1/4. Wha

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Question 1071971: The probability that Olivia will have to wait before she can cross Westgate Street is 1/3 and the probability that she will be able to cross high street without waiting is 1/4. What is the probability that :-
A. She does not have to wait to cross Westgate Street.
B. She has to wait to cross high street.
C. She can cross both streets without waiting.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
probability to wait before crossing westgate street is 1/3.
probability to cross high street without waiting is 1/4.

for westgate street:

p(wait) = 1/3
p(no wait) = 1 - 1/3 = 2/3

for high street:

p(wait) = 1 - 1/4 = 3/4
p(no wait) = 1/4

your questions answered below:

A. She does not have to wait to cross Westgate Street.

p(no wait) = 2/3.

B. She has to wait to cross high street.

p(wait) = 3/4.

C. She can cross both streets without waiting.

p(nowait at westgate street) = 2/3
p(nowait at high street) = 1/4

p(nowait at westgate street and at high street) = 2/3 * 1/4 = 2/12 = 1/6