The probability that a driver stopping at petrol station

TomJerry

Question:
The probability that a driver stopping at petrol station will have only his car tyre checked is 0.012, the probability that he will have the oil checked is 0.29 and the probability that he will have both oil and tyre's checked is 0.07. What is the probability that a driver stopping at the station will have neither his car tyres nor oil checked

Solution:

Let A be he checks his tyres
P(A) = 0.012
P(A') = 1 - 0.012

Let B be he checks oil
P(B) = 0.29
P(B') = 1 - 0.29

P(A intersection B) = 0.07

We need to find P(A' union B')

P(A' union B') = P(A') + P(B') - P(A' intersection B')

I m stuck here dont know how to go forward from here

tiny-tim

Hi TomJerry!

Hint: P(A) = P(A and B) + P(A and not-B)

(or just draw a Venn diagram and measure the area)