John asked in Science & MathematicsMathematics · 8 years ago

Probability Car not starting?

During the winter a man has trouble starting his two cars. The probability that car 1 starts is .8 and the probability that car 2 starts is .45. There is a probability of .35 that both cars starts.

a. What is the probability that at least one car starts

b. What is the probability that neither car starts

c. What is the probability that Car 1 starts but Car 2 does not?

d. What is the probability that exactly one car starts?

Relevance
• 8 years ago

We can break this down into four cases: both start, neither starts, 1 starts and 2 doesn't, and 2 starts and 1 doesn't. These cases don't overlap, and they cover all the possibilities.

Probabilities for these cases are:

Both cars start: 0.35 (given)

1 starts and 2 doesn't: 0.8 - 0.35 = 0.45

2 starts and 1 doesn't: 0.45 - 0.35 = 0.10

Neither starts: 1 - (0.35 + 0.45 + 0.10) = 1 - 0.90 = 0.1

With these computed, we can answer each question easily:

a. What is the probability that at least one car starts

This is the probability that we don't have the case where neither starts, so it's

1 - 0.1 = 0.9

b. What is the probability that neither car starts

0.1 (computed above)

c. What is the probability that Car 1 starts but Car 2 does not?

0.45 (computed above)

d. What is the probability that exactly one car starts?

Add up the two one-car-starts cases:

0.45 + 0.10 = 0.55