Answer:
a) 0.5476
b) 0.0676
c) 0.4524
Step-by-step explanation:
Given this information, we can conclude that 74% of the cars won't need any repairs over a 1-year period (100 - 20 - 5 - 1 = 74%). And 26% will need at least 1 repair over a 1-year period.
P(car doesn't need repair) = 0.74
P (car needs repair) = 0.26
If you own two cars, the probability that:
<u>a) Neither will need repair:</u>
We need that car 1 won't need repair AND car 2 won't need repair.
=P(Car 1 doesn't need repair) x P(Car 2 doesn't need repair)
= 0.74 x 0.74 = 0.5476
The probability that neither will need repair is 0.5476.
<u>b) Both will need repair:</u>
We need that car 1 needs repair AND car 2 needs repair.
P(Car 1 needs repair) x P(Car 2 needs repair)
= 0.26 x 0.26 = 0.0676
The probability that both will need repair is 0.0676
<u>c) At least one car will need repair</u>
Car 1 needs repair or Car 2 needs repair or both need repair.
To solve this one, it's easier to use the complement of P(neither needs repair)
1 - P(neither needs repair)
1 - (0.74)(0.74) = 1 - 0.5476 = 0.4524
The probability that at least one car will need repair is 0.4524
