razzy02
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A car is due to have three safety tests.

The probability that the brakes will fail is 1/4
The probability that the steering will fail is 1/10 The probability that the lights will fail is 1/5
These three events are independent.
Calculate the probability that the car fails only one of the three tests.
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RDKGames
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(Original post by razzy02)
A car is due to have three safety tests.

The probability that the brakes will fail is 1/4
The probability that the steering will fail is 1/10 The probability that the lights will fail is 1/5
These three events are independent.
Calculate the probability that the car fails only one of the three tests.
So if we denote the events for failure of brakes, steering and lights as B, S, L, and their passes as B', S', L' then we clearly we have:

P(B) = 0.25 \Rightarrow P(B' )=0.75
P(S) = 0.1 \Rightarrow P(S' ) = 0.9
P(L) = 0.2 \Rightarrow P(L' )= 0.8

We are looking for P(B \cap S' \cap L' )+ P(B' \cap S \cap L' )+ P(B' \cap S' \cap L).
You can use the fact that these events are independent to answer this.
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