An aerospace company has submitted bids on two separate federal government defen

Question

An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 40% probability of winning the first con- tract. If they win the first contract, the probability of winning the second is 65%. However, if they lose the first contract, the pres- ident thinks that the probability of winning the second contract decreases to 49%.

A. What is the probability that they win both contracts? Probability =
B.What is the probability that they lose both contracts? Probability =

C. What is the probability that they win only one contract? Probability =

Explanation / Answer

P( winning the first conntract ) = 0. 40       P ( winning the second contract ) =0.65

A]

P( win both contracts ) = P ( winning the first conntract And winning the second contract )

= P ( winning the first conntract ) P( winning the second contract )

         = 0.40*0.65 = 0.26

Final answer for A ]

P( win both contracts ) = 0.26

B ]

    P ( lossing the first contract ) = 1 - P( winning the first conntract ) = 1 - 0.40 = 0.60

If they lose the first contract, the pres- ident thinks that the probability of winning the second contract decreases to 49% ( i. e 0.49 )

P (they lose both contract) = P ( lossing the first conntract And then lossing the second contract )

                                            = 0.60 *( 1- 0.49 )= 0.306

Final answer for B ]

P(they lose both contracts ) = 0.306

C ]

P(win one)=probability of winning first losing second +probability of losing first winning second

               = 0.40 * 0.35    + 0.60 *0.49 = 0.434

Final answer for C ]

P(win one) = 0.434 .

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