Question

The weather during a Bloodhound game is somewhat unpredictable. It may be sunny, cloudy or rainy. The probability of sunny weather is 0.42. The probability of cloudy weather is 0.38. The probability of rainy weather is .20. John Jay, mighty center-fielder for the Bloodhounds, is colorblind. Thus, if it is sunny, he has a 0.19 probability of hitting a home run in a game; if it cloudy, he has a 0.12 probability of hitting a home run in a game; if it is rainy, he has a 0.17 probability of hitting a home run in a game. The Bloodhounds play a game, say G.

a. What is the probability that John Jay hits a home run in G
b. What is the probability that John Jay does not hit a home run in G?
c. Find the conditional probability that John Jay hits a home run in G given that it rains?
d. What is the probability that it rains, and John Jay hits a home run?
e. If John Jay hits a home run, what is the probability that it rained?
f. If weather is independent from day to day then what is the probability that it is sunny 3 days in a row.

Answer 1

Given:

P(Sunny Weather) = P(S) = 0.42

P(Cloudy Weather) = P(C) = 0.38

P(Rainy Weather) = P(R) = 0.20

and

P(hit a home run given Sunny Weather) = P(h|S) = 0.19

P(hit a home run given Cloudy Weather) = P(h|C) = 0.12

P(hit a home run given Rainy Weather) = P(h|R) = 0.17

a)

The probability that John Jay hits a home run in G = P(h)

Using the law of total probability,

b)

The probability that John Jay does not hit a home run in G = P(h')

c)

The conditional probability that John Jay hits a home run in G given that it rains = P(h|R)

d)

The probability that it rains and John Jay hits a home run = P(h and R)

using the conditional probability law,

e)

If John Jay hits a home run, the probability that it rained =P(R|h)

using the conditional probability law,

f)

The probability that it is sunny 3 days in a row P(R1 and R2 and R3)

using the independence of probability law,

e. If John Jay hits a home run, what is the probability that it rained?
f. If weather is independent from day to day then what is the probability that it is sunny 3 days in a row.