Use the following information to answer the next ten exercises. Forty-eight perc
ID: 3048381 • Letter: U
Question
Use the following information to answer the next ten exercises. Forty-eight percent of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder. Among Latino California registered voters, 55% prefer life in prison without parole over the death penalty for a person convicted of first degree murder. 37.6% of all Californians are Latino.
In this problem, let:
• C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first degree murder.
• L = Latino Californians
Suppose that one Californian is randomly selected.
44. Find P(C).
45. Find P(L).
46. Find P(C|L).
47. In words, what is C|L?
48. Find P(L AND C).
49. In words, what is L AND C?
50. Are L and C independent events? Show why or why not.
51. Find P(L OR C).
52. In words, what is L OR C?
53. Are L and C mutually exclusive events? Show why or why not.
Please show all work.
Explanation / Answer
44. P(C) = 48% = 0.48
This follows from the problem statement that 48% of all Californians registered voters prefer life in prison without parole over the death penalty for a person convicted of first degree murder.
45. P(L) = 37.6% = 0.376
37.6% of all Californians are Latino
46. P(C|L) = 55% = 0.55
Among Latino California registered voters, 55% prefer life in prison without parole over the death penalty for a person convicted of first degree murder.
47. C|L is the event that a Californian registered voter is in favor of life in prison without parole given that that person is a Latino.
48. P(L and C) = P(C|L) * P(L) = 0.55 * 0.376 = 0.2068
This follows from the Bayes' theorem about conditional probability.
49. L and C is the event that a Californian registered voter is both a Latino as well as in favour of life in prison without parole.
50. L and C are not independent events.
For them to be independent, the conditional probability has to be equal to the unconditional probability. Here, P(C|L) = 0.55 != 0.48 = P(C)
51. P(L or C) = P(L) + P(C) - P(L and C) = 0.376 + 0.48 - 0.2068 = 0.6492
52. L or C is the event that a Californian registered voter is either in favor of life in prison without parole or is a Latino or both.
53. L and C are not mutually exclusive events.
For them to be mutually exclusive, the joint probability will have to be zero. That will happen here if there would be no Californian registered voter who would both be a Latino as well as in favour of life in prison without a parole. Here P(L and C) != 0.