Answer:
0.8 = 80% probability that he drove the small car
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Being at work on time.
Event B: Driving the small car.
Probability of being at work on time:
0.8 of 0.75(small car).
0.6 of 0.25(large car). So
[tex]P(A) = 0.8*0.75 + 0.6*0.25 = 0.75[/tex]
At work on time, using the small car:
0.8 of 0.75
So
[tex]P(A \cap B) = 0.8*0.75 = 0.6[/tex]
What is the probability that he drove the small car
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.6}{0.75} = 0.8[/tex]
0.8 = 80% probability that he drove the small car
