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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)?

Guest Feb 4, 2019

#1**+1 **

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

CPhill Feb 4, 2019

#2**+2 **

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%**

Guest Feb 4, 2019