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Integers a, b, c, and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad-bc is even?

 

Jack rolls 5 fair six-sided dice. What is the probability that at least two dice show the same number?

 

The probability of getting rain on any given day in June in Capital City is 1/10. What is the probability that it rains on at most 2 days in June? Express your answer as a decimal to the nearest thousandth.

 

Carson flips over the cards of a standard 52-card deck one at a time. What is the probability that he flips over the ace of spades before any face card (jack, queen or king)?

 Feb 4, 2019
 #1
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The probability of getting rain on any given day in June in Capital City is 1/10. What is the probability that it rains on at most 2 days in June? Express your answer as a decimal to the nearest thousandth.

 

P  ( rain 0 days ) =   (.9)^30

 

P (rain 1 day ) =  C(30, 1)(.1)(.9)^29 

 

P(rain on 2 days) = C(30, 2) (.1)^2 (.9)^28

 

So...P(rain at most 2 days ) =

 

(.9)^30 +  C(30, 1)(.1)(.9)^29  + C(30, 2) (.1)^2 (.9)^28  ≈   .4114

 

cool cool cool

 Feb 4, 2019
 #2
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Jack rolls 5 fair six-sided dice. What is the probability that at least two dice show the same number?

1st die - any number, or.................................................................. = 6/6
2nd die-probability that it is different from the first......................     =5/6
3rd die-................................................................................1st two =4/6
4th die-...............................................................................1st three =3/6
5th die-................................................................................1st four =2/6
So, the probability that they are all different from each other =6/6 x 5/6 x 4/6 x 3/6 x 2/6 =6! / 6^5 =0.09259.
And the probability that at least 2 of them show the same number =1 - 0.09259 =90.74%

 Feb 4, 2019

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