Answer:
a)
Represent the probability that the event B occurs given that the event A occurs first
b)
Represent the probability that the event B no occurs given that the event A occurs first
c)
Represent the probability that the event A occurs given that the event B occurs first
d)
Represent the probability that the event A no occurs given that the event B occurs first
Step-by-step explanation:
For this case we have the following probabilities given for the events defined A and B
For this case we can begin finding the probability for the complements:
For this case we are interested on the following probabilities:
Part a
For this case we can use the Bayes theorem and we can find this probability like this:
Represent the probability that the event B occurs given that the event A occurs first
Part b
And for this case we can find
And if we replace we got:
Represent the probability that the event B no occurs given that the event A occurs first
Part c
Represent the probability that the event A occurs given that the event B occurs first
Part d
And for this case we can find
And if we replace we got:
Represent the probability that the event A no occurs given that the event B occurs first