The probability that a driver stopping at petrol station

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SUMMARY

The probability that a driver stopping at a petrol station will have neither his car tyres nor oil checked is calculated using the provided probabilities. Given P(A) = 0.012 for tyre checks, P(B) = 0.29 for oil checks, and P(A ∩ B) = 0.07 for both checks, the solution involves determining P(A' ∪ B'). The final calculation reveals that the probability of neither event occurring is 0.673. This conclusion is reached by applying the formula P(A' ∪ B') = P(A') + P(B') - P(A' ∩ B').

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TomJerry
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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 don't know how to go forward from here
 
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Hi TomJerry! :smile:

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

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

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