A student figures that he has a 69 % chance of being let out of class late. If he leaves class late, there is a 84 % chance that he will miss his train. What is the probability that he gets out of class late and misses the train?

P (MT and L) = P (Late) * P (MT) = 0.69*0.84 = 0.5796

So then we have a 57.96 % of chance of being late and miss the train.

Step-by-step explanation:

Data given

Let's define the following events:

L = Being late, MT = Miss the train

For this case we have the following probabilities given:

P (L) = 0.69, P (MT|L) = 0.84

And for this case we can assume that is possibe miss the train just and only if we are late.

The multiplication rule (general multiplication rule) "is a way to find the probability of two events happening at the same time"

Let A and B two events. From the general multiplication rule we have this formula:

P (A and B) = P (B|A) P (A) = P (A|B) P (B)

Solution for the problem

For this case we want to find this probability P (MT and T)

And we can use the previous rule and we have this:

P (MT and L) = P (Late) * P (MT) = 0.69*0.84 = 0.5796

So then we have a 57.96 % of chance of being late and miss the train.