You are given the information that P(A) = 0.30 and P(B) = 0.40. Do you have enou

Question

You are given the information that P(A) = 0.30 and P(B) = 0.40. Do you have enough information to compute P(A and B)? Explain. No. You need to know P (A or B). Yes. This probability is equal to 0.12. No. You need to know if the events are independent or the value of P(A | B) or P{B | A). No. You need to know if the events are mutually exclusive. If you know that events A and B are independent, do you have enough information to compute P(A and B)? Explain. Yes. For independent events, P(A and B) = P(A) middot P(B) + P(B | A). No. Knowing the events are independent does not provide any extra information. Yes. For independent events, P(A and B) = 0. Yes. For independent events, P(A and B) = P(A) middot P(B). Does it pay to ask for a raise? A national survey of heads of households showed the percentage of those who asked for a raise and the percentage who got one. According to the survey, of the women interviewed, 26% had asked for a raise, and of those women who had asked for a raise, 45% received the raise. If a woman is selected at random from the survey population of women, Find the following probabilities. (Enter your answers to three decimal places.) P (woman asked for a raise) P (woman received raise, given she asked for one) P (woman asked for raise and received raise)

Explanation / Answer

3.

(a)P(A) = 0.30 P(B) =0.40

Do you have enough information to compute P(A and B)

By multiplication theorem,

P(A and B ) = P(A) .PB|A) or P(A and B) = P(B) P(A|B)

When A and B events are independent P(A|B) = P(A) ; P(B|A) = P(B)

So the answer is

No. you need to know if the events are independent or the value of P(A|B) or P(B|A)

(b) .If you know the Events A and B are independent , do you have enough information to compute P(A and B)

Yes. For independent event P(A and B) = P(A) . P(B).

4. % women asked for raised(of the women interviewed) = 26%

A: Event of women asking for raise

P(Women asked for raised) =  % women asked for raised / 100 = 26/100 = 0.26

B: Event of women received raise

% women received raise (of those women asked for raise) = 45%

% women received raise | Given the women asked for raise =45%

P(B|A) = (% women received raise | Given the women asked for raise) / 100 = 45/100 = 0.45

(c) P(Women Asked for raise andd received raise) = P(A and B)

By multiplication theorem of probability

P(A and B) = P(A) x P(B|A) = 0.26 x 0.45 = 0.117

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