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 A toy has three parts, L, M and N, whose chances of being defective are 3%, 4% and 2% respectively. The toy is of no use if any one of the parts becomes defective. What is the probability that the toy will not stop working?

 A toy has three parts, L, M and N, whose chances of being defective are 3%, 4% and 2% respectively. The toy is of no use if any one of the parts becomes defective. What is the probability that the toy will not stop working? Correct Answer 0.9

Concept:

P(A ⋃ B ⋃ C) = P(A) + P(B) + P(C) – P(A ⋂ B) – P(B ⋂ C) – P(A ⋂ C) + P(A ⋂ B ⋂ C)

 

Calculation:

Here, P(L) = 0.03, P(M) = 0.04, P(N) = 0.02

Probability that toy stops working

P(L ∪ M ∪ N) = 0.03 + 0.04 + 0.02 - (0.03 × 0.04) - (0.04 × 0.02) - (0.03 × 0.02) + 0.03 × 0.04 × 0.02

= 0.09 - 0.0012 - 0.0008 - 0.0006 + 0.000024

= 0.087

Probability that the toy will not stop working

1 - P(L ∪ M ∪ N) = 1 - 0.087

= 0.9

Hence , option (3) is correct.

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