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the boston weatherman says there is a 75 percent chance of rain for each day of the labor day four-day weekend. if it doesn't rain, then the weather will be sunny. paul and yuri want it to be sunny one of those days for a world war iii preenactment, but if it's sunny for more than one day they won't know what to do with themselves. what is the probability they get the weather they want? give your answer as a fraction.

Sagot :

The probability that Paul and Yuri get the weather they want = 27/64

Given probability for rain = 75% = 3/4

The total probability is considered as 100% or 1.

So the probability for sunny day = 1 - 3/4 = 1/4

Paul and Yuri want a sunny day from labor day 4 -day weekend.

This means 3 days of rain and 1 sunny day. So 3 times the probability for rain and 1 time the probability for sunny day.

This one sunny day can be chosen from 4 days. In other ways there is 4C1 =4 different ways possible to choose 3 days of rain and 1 sunny day from 4 days.

So finally the probability that Paul and Yuri get the weather they want

= [tex]\frac{3}{4}^3 \times \frac{1}{4} \times 4[/tex] = 27/64

Learn more about probability at https://brainly.com/question/24756209

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