3 Pablo drives to work The probability that he leaves home before 0700 is 34If he leaves home before 0700 the probability he will be late for work is 18If he leaves home at 0700 or later the probabili

We can use Bayes' theorem to solve this problem:

Let A be the event that Pablo leaves home before 07:00, and B be the event that he is late for work. We want to find P(A|B), the probability that Pablo left home before 07:00 given that he is late for work.

Using the law of total probability, we can calculate the probability of being late for work as:

P(B) = P(A)P(B|A) + P(A')P(B|A')

where A' is the complement of A (i.e. the event that Pablo leaves home at 07:00 or later).

Substituting the given probabilities, we have:

P(B) = (3/4)(1/8) + (1/4)(5/8) = 11/32

Now we can use Bayes' theorem to find P(A|B):

P(A|B) = P(A)P(B|A) / P(B)

Substituting the given probabilities, we have:

P(A|B) = (3/4)(1/8) / (11/32) ≈ 0.068

Therefore, the probability that Pablo left home before 07:00 given that he is late for work is approximately 0.068, or about 6.8%