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Two dice are thrown. What is the probability that the first die rolls a 1 if it is known that the number of points on the second die is higher than on the first?
From a pocket containing 10 coins (20 cents each) and 10 coins (3 cents each), 10 coins are taken randomly. What is the probability that the amount of money left in the pocket is not less than the one taken out
The multiple-choice question on a combinatorics quiz contains 20 questions with ten possible answers each (where only 1 answer is true). Compute the probability of randomly guessing the correct answers and getting at least 10 correct answers to 20 questions (Event A). Find the mathematical expectation and variance of the number of correct answers.
Let S = {w1,w2,...,wk} be a basis for the vector space V. Prove that every vector in V can
be expressed as a linear combination of vectors w1,w2,...,wk
in exactly one .
Two boxes, 1 and 2 are given. Suppose box 1 contains 6 black and 7 white balls. Box 2 contains 9 black and 8 white balls. Three balls are selected at random from box 1 and put into box 2. Then two balls are selected at random from box 2.
1) what is the probability that these two balls have the same color
2) what is the probability that these two balls have the different colors
