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)?
+130536 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
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%
