Let E be the event that a new car requires engine work under warranty and let T

Question

Let E be the event that a new car requires engine work under warranty and let T be the event that the car requires transmission work under warranty. Suppose that P(E) = 0.10, P(T) = 0.02 and P(T intersection E) = 0.01. Find the probability that the car needs work on either the engine, the transmission or both. Find the probability that neither the engine nor the transmission needs work. P(A union B) = P(A) + P(B) - P(A intersection B) P(E union T) = 0.10 + 0.02 - 0.01 1 - .11 = .89 A computer consulting firm presently has bids out on 3 projects. Let Ai = [awarded project i). for i = 1, 2, 3, and suppose that P(AI) = .22.P(A2) = .25. P(A3) = .28. P(Al intersection A2) = .11. P(A1 intersection A3) = .05. P(A2 intersection A3) = .07. P(A1 intersection A2 intersection A3) = .01. Compute the probability of event 1) (A1^* intersection A2*) intersection A3. and 2) (A1^* intersection A2^*) union A3.

Explanation / Answer

2.

a)

Hence, in other words, it is asking for P(E U T).

P(E U T) = P(E) + P(T) - P(E n T)

= 0.10 + 0.02 - 0.01

= 0.11 [ANSWER]

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b)

Hence,

P(E' n T') = 1 - P(E U T)

= 1 - 0.11

= 0.89 [ANSWER]

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