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For a bill to come before the president of the United States, it must be passed by both the House of Representatives and the Senate. Assume that, of the bills presented to these two bodies, 60 percent pass the House, 80 percent pass the Senate, and 90 percent pass at least one of the two.
Calculate the probability that the next bill presented to the two groups will come before the president.

Respuesta :

Answer:

0.50

Step-by-step explanation:

Given that for a bill to come before the president of the United States, it must be passed by both the House of Representatives and the Senate.

Assume that, of the bills presented to these two bodies, 60 percent pass the House, 80 percent pass the Senate, and 90 percent pass at least one of the two.

A- Event that the bill passes the house

B - Event that the bill passes the senate

Then we are given that

[tex]P(A) = 0.60\\P(B) = 0.80\\P(AUB) = 0.90[/tex]

By addition theorem of probability we have

[tex]P(AUB) = P(A)+P(B)-P(A\bigcap B)\\0.90 = 0.60+0.80-P(A\bigcap B)\\P(A\bigcap B)=0.50[/tex]

Hence probability that the next bill presented to the two groups will come before the president =

Prob for both

= 0.50

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