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A university graduate has applied for two jobs at company A and B. The graduate feels that she has a 65% chance of getting a job at company A and a 40% chance of getting a job at company B.if she gets a job offer from B, she believes that she has 70% chance of getting a job at A

What is the probability that both companies offer her a job?

What is the probability exactly one company offer her a job?

If she gets a offer from company A what is the probability that she will not receive a offer from B?

Macro
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Matthew
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  • Since this is clearly a homework problem, can you please tell us where your confusion lies? What have you tried? – Macro Jan 18 '13 at 18:37
  • The Confusion with the 70% adjustment as well as the last question – Matthew Jan 18 '13 at 18:40
  • for the first my attempt was 0.65*0.4 +04*0.7 – Matthew Jan 18 '13 at 18:43
  • Ok, well if you let $A,B$ be the events that the person gets a job at companies A, B respectively, then the definition of conditional probability tells you that $P(A \ {\rm and} \ B) = P(A|B) \cdot P(B)$. Where do you go from there? – Macro Jan 18 '13 at 18:45
  • 0.7*0.4 , but what about if A offers first? – Matthew Jan 18 '13 at 18:47
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    Jason, I don't think time is an element of this problem. In any case, if the problem were reversed (and you were instead told $P(B|A)$) then you should get the same answer since the definition of conditional probability also tells you that $P(A \ {\rm and} \ B) = P(B|A) \cdot P(A)$. – Macro Jan 18 '13 at 18:54
  • My Thinking was as such $P( A \text{ and } B \text{ if A offers first}) + P( A \text{ and } B \text{ if B offers first})$. Hence $ 0.65*0.4 +0.4*0.7$ – Matthew Jan 18 '13 at 18:57
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    Hint: You can solve this problem by drawing a figure like the right hand one at http://stats.stackexchange.com/questions/47671/what-is-the-difference-between-using-the-multiplication-rule-or-using-venn-diagr/47800#47800. (The two dimensions of the rectangle correspond to "Receives offer from A" and "Receives offer from B.") Your question is *almost* identical to the second half of http://stats.stackexchange.com/questions/47671. There, a conjunctive probability (0.10) is given; here, a conditional probability (0.70) is. – whuber Jan 18 '13 at 19:35
  • Jason, you should recognize this immediately as an application of Bayes' rule and use probability notation to indicate the various events in the problem description. – AdamO Jan 18 '13 at 19:38

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