Question

In: Statistics and Probability

In a recent survey about US policy in Iraq, 62 % of the respondents said that...

In a recent survey about US policy in Iraq, 62 % of the respondents said that they support US policy in Iraq. Females comprised 53% of the sample, and of the females, 46% supported US policy in Iraq. A person is selected at random.

What is the probability that the person we select is female and supports U.S. policy in Iraq?
Are the events "does not support U.S, policy in Iraq" and "female" statistically independent? Why or why not?
What is the probability that the person we select is male?
What is the probability that the person we select does not support US policy in Iraq?
What is the probability that the person we select is female and does not support US policy in Iraq?
What is the probability that the person we select is male and does support US policy in Iraq?
What is the probability that the person we select is male and does not support US policy in Iraq?
Suppose we select a supporter of US policy in Iraq, what is the probability that the person we select is female?
) Suppose we select a person who does not support US policy in Iraq, what is the probability that the person is male?

Solutions

Expert Solution

a) What is the probability that the person we select is female and support US policy in Iraq?

ans:Event S: Support US policy in Iraq, E vent F:Female

F(S) = 0.62, P(F) =0.53 and P(S|F) = 0.46

therefore,

P(F∩S) = P(S| F)*P(F) = (0.46)(0.53) = 0.2438

b)Are the events “does not support US policy in Iraq” and “female” statistically independent? Why or why not?

ans: P(F| S) = P(F∩S) / P(S) = 0.2862 / 0.38 = 0.753 and P(F) = 0.53

Since P(F| S) *P(F), the events “ does not support US policy in Iraq” and “female” are not statistically independent.

c) What is the probability that the person we select is male?

ans:Event M: Male

P(M) = 1 – P(F) = 1 – 053 = 0.47

d) What is the probability that the person we select does not support US policy in Iraq?

ans:

US Policy in Iraq

	Support	Doesn't Support	Row Total
Female	0.2438	0.2862	0.53
Male	0.3762	0.0938	0.47
Column Total	0.62	0.38	1.00

e) What is the probability that the person we select is female and doe not support US policy in Iraq?

ans:P(F) = P(F I S) + P(F I S)*0.53 = 0.2438 + P(F I S).

Hence, P(F I S) = 0.2862.

f)What is the probability that the person we select is male and supports US policy in Iraq?

ans: P(S) = P(S I F) + P(S I M) *0.62 = 0.2438 + P(S I M).

Hence, P(S I M) = 0.3762

g)What is the probability that the person we select is male and does not support US policy in Iraq?

ans: P(M) = P(M I S) + P(M I S)*0.47 = 0.3762 + P(M I S).

Hence, P(M I S) = 0.0938.

h) Suppose we select a supporter of US policy in Iraq, what is the probability that the person we select is female?

ans: P(F | S) = P(F I S) / P(S) = 0.2438 / 0.62 = 0.393

i) Suppose we select a person who does not support US policy in Iraq, what is the probability that the person is male?

ans: P(M | S) = P(M I S) / P(S) = 0.0938 / 0.38 = 0.247

orchestra answered 1 year ago

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