The probability that it will rain tomorrow is 14. The probability that Chris will be late to his office given that it does not rain tomorrow is 56 and the probability that Chris will be late to his office given that it rains tomorrow is 23. What is the probability that it will rain tomorrow, given that Chris is not late to his office?

To solve this problem, we can use Bayes' theorem. Bayes' theorem states that the probability of an event A given event B can be calculated using the formula:

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

In this case, we want to find the probability that it will rain tomorrow (event A), given that Chris is not late to his office (event B). Let's assign the following probabilities:

P(A) = Probability that it will rain tomorrow = 14 P(B|A) = Probability that Chris is not late to his office given that it rains tomorrow = 1 - 23 = 77 P(B) = Probability that Chris is not late to his office

To find P(B), we need to consider the probabilities of Chris being late to his office in both scenarios: when it rains and when it does not rain.

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

Where A' represents the event that it does not rain tomorrow.

P(B|A') = Probability that Chris is not late to his office given that it does not rain tomorrow = 1 - 56 = 44 P(A') = Probability that it does not rain tomorrow = 1 - 14 = 86

Now we can substitute these values into the equation to find P(B):

P(B) = (44 * 86 + 77 * 14) / 100

Calculating this expression, we find that P(B) = 54.2.

Finally, we can use Bayes' theorem to find the probability that it will rain tomorrow given that Chris is not late to his office:

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

P(A|B) = (77 * 14) / 54.2

Calculating this expression, we find that P(A|B) ≈ 19.9.

Therefore, the probability that it will rain tomorrow, given that Chris is not late to his office, is approximately 19.9%.