Car repairs: Let be the event that a new car requires engine work under warranty and let be the event that the car requires transmission work under warranty. Suppose that ,P(E) = 0.10 , P(T) = 0.02 and P(E, T) = 0.01 . (a) Find the probability that the car needs work on either the engine, the transmission, or both.
(b) Find the probability that the car needs no work on the engine.

a) 0.11 =  11% probability that the car needs work on either the engine, the transmission, or both.

b) 0.9 = 90% probability that the car needs no work on the engine.

Step-by-step explanation:

P(E) = 0.10 , P(T) = 0.02 and P(E,T) = 0.01 .

This means that:

Only engine: 0.1 - 0.01 = 0.09

Only transmission: 0.02 - 0.01 = 0.01

Both engine and transmission: 0.01

(a) Find the probability that the car needs work on either the engine, the transmission, or both.

0.09 + 0.01 + 0.01 = 0.11

0.11 =  11% probability that the car needs work on either the engine, the transmission, or both.

(b) Find the probability that the car needs no work on the engine.

Probability of needing work on engine:

0.09 + 0.01 = 0.1

Not needing:

1 - 0.1 = 0.9

0.9 = 90% probability that the car needs no work on the engine.