Q.1. The probability that a driver stopping at petrol station will have his car tyres checked is 0.12 , the probability that he will have oil checked is 0.29 and probability that he will have both oil and tyres checked is 0.07. What is the probability that a driver stopping at the station will have neither his car tyres nor oil checked?
Answers
Given : probability that a driver stopping at petrol station will have his car tyres checked is 0.12 , the probability that he will have oil checked is 0.29 and probability that he will have both oil and tyres checked is 0.07
To find : probability that a driver stopping at the station will have neither his car tyres nor oil checked
Solution:
Probability car tyres checked P(T) = 0.12
probability oil checked P(O) = 0.29
probability both oil and tyres checked P(T ∩ O ) = 0.07
Probability None of These P(None) = ?
Total = P(T) + P(O) - P(T ∩ O ) + P(None)
We know total probability is always 1
=> 1 = 0.12 + 0.29 - 0.07 + P(none)
=> 0.66 = P(none)
probability that a driver stopping at the station will have neither his car tyres nor oil checked = 0.66
or probability that a driver stopping at the station will have neither his car tyres nor oil checked = 1 - P (T U O )
P (T U O ) = P(T) + P(O) - P(T ∩ O ) = 0.12 + 0.29 - 0.7 = 0.34
=> 1 - 0.34 = 0.66
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