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On rainy days, Joe is late to work with probability .3; on
Chapter 3, Problem 33P(choose chapter or problem)
Problem 33P
On rainy days, Joe is late to work with probability .3; on nonrainy days, he is late with probability .1. With probability .7, it will rain tomorrow.
(a) Find the probability that Joe is early tomorrow.
(b) Given that Joe was early, what is the conditional probability that it rained?
Questions & Answers
QUESTION:
Problem 33P
On rainy days, Joe is late to work with probability .3; on nonrainy days, he is late with probability .1. With probability .7, it will rain tomorrow.
(a) Find the probability that Joe is early tomorrow.
(b) Given that Joe was early, what is the conditional probability that it rained?
ANSWER:
Step 1 of 2
Joe is late to work with probability .3 on a rainy day.
Let L denotes that the event that Joe is late to work.
Let R denotes that the it rains.
Let E denotes that the Joe is early to work.
So here the probability of E is
P(E) = 1-P(L).
We consider,
P = 0.3
P = 0.1
P = 0.7
Our goal is
a). We need to find the probability that Joe is early tomorrow.
b). We need to find the conditional probability that it rained.
a). Now we have to find the probability that Joe is early tomorrow.
P(E) = P()
P(E) = 1-P(L)
P(L) =
P(L) =
P(L) =
P(L) =
P(L) =
P(E) = 1-0.24
P(E) = 0.76
Therefore, the probability that Joe is early tomorrow is 0.76.