Question

A Field Poll Survey reported that 67% of registered voters in a state approved of allowing two people of the same gender to marry and have regular marriage laws apply to them. Among 18 to 39 year olds (registered voters in this state), the approval rating was 72%. Seven in ten registered voters in this state said that the upcoming Supreme Court's ruling about the constitutionality of a proposition was either very or somewhat important to them. Out of those registered voters who support same-sex marriage, 75% say the ruling is important to them. In this problem, let the following apply.

•	C = registered voters who support same-sex marriage
•	B = registered voters who say the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them
•	A = registered voters who are 18 to 39 years old.

*Please show step by step on how to get the correct answers.

• Find P(C AND B). (Enter your answer to four decimal places.)
  P(C AND B) =  

• Find P(C OR B).
  P(C OR B) =  

Answer 1

The proportion of registered voters in a state who approved two people of the same gender to marry and have regular marriage laws apply to then is P2 = 0.67. The proportion of registered voters among age 18 to 39-year-old who approved the same gender marriage is P2 = 0.72. The proportion of registered voters who said that the upcoming Supreme Court's ruling about the constitutionality of a proposition was either very or somewhat important to them is P==0.7. The proportion of registered voters who support the same sex marriage say that the ruling is important to them is pe = 0.75. Consider the following events: C= registered voters who support same-sex marriage. B = registered voters who say the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them. A = registered voters who are 18 to 39 years old. From the above information, the probabilities are as follows: P(C)= P1 = 0.67, P(B) = p; = 0.7, P(CA)= P2 = 0.72,P(B|C)= P4 =0.75. The value of P(C AND B) is equivalent to the probability of the registered voters who support same sex marriage and say that the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them. From the definition of the conditional probability, the value of P(C AND B) is calculated as follows: P(BIC)-P(C AND B) P(BC)== P(C) = P(C AND B) = P(BIC) P(C) =P(C AND B) = 0.75x0.67 = P(C AND B)=0.5025 The value of P(COR B) is equivalent to the probability of the registered voters who support same sex marriage or say that the Supreme Court's ruling about the constitutionality of the proposition is very or somewhat important to them. From the definition of the probability of union of two events, the value of P(CORB) is calculated as follows: P(COR B)=P(C)+P(B)-P(C AND B) = 0.67 +0.7 – 0.5025 (From 1.) PIC OR B) = 0.8675