Question

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.

Answer 1

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.