In: Statistics and Probability
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