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

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(E and T) = 0.01. Find the probability that the car needs work on either the engine, the transmission, or both.

Answer 1

To find the probability that the car needs work on either the engine, the transmission, or both, we can use the principle of inclusion-exclusion.

The probability that the car needs work on either the engine or the transmission (or both) can be calculated as follows:

𝑃(𝐸∪𝑇)=𝑃(𝐸)+𝑃(𝑇)−𝑃(𝐸∩𝑇)

Given:

1. 𝑃(𝐸)=0.10
2. 𝑃(𝑇)=0.02
3. 𝑃(𝐸∩𝑇)=0.01

Now, let's plug these values into the formula:

𝑃(𝐸∪𝑇)=0.10+0.02−0.01

𝑃(𝐸∪𝑇)=0.11

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