Question 5
a) Explain the significance of P(A or B) = P(A) + P(B) – P(A and B) as addition rule in probability. At what stage would P(A or B) = P(A) + P(B), and what is the rationale behind this? CR (5 marks)
b) 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. Let C = Californians (registered voters) preferring life in prison without parole over the death penalty for a person convicted of first-degree murder. Let L = Latino Californians. Suppose that one Californian is randomly selected. Determine P(C/L) and explain the reason behind your answer. AN (7 marks)
c) Explain the dichotomy between mutually exclusive event and dependent event in a probability distribution.
a) The addition rule states the probability of two events is the sum of the probability that either will happen minus the probability that both will happen:
"P(A\\lor B)=P(A)+P(B)-P(A\\land B)"
If A and B are disjoint, then "P(A\\land B)=0" ,
so the formula becomes "P(A\\lor B)=P(A)+P(B)" (events A and B cannot occur at the same time).
b) "C|L" means, given the person chosen is a Latino Californian, the person is a registered voter who prefers life in prison without parole for a person convicted of first degree murder.
Using Multiplication Rule:
"P(C|L)=0.55=55\\%"
c) Two events are mutually exclusive if the probability that they both happen at the same time is zero.
Dependent events: the occurrence of one event has effect on the probability of the occurrence of another event.
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