A box B1, contains 1 white ball, 3 red balls and 2 black balls. Another box B2, contains 2 white balls, 3 red balls and 4 black balls. A third box B3, contains 3 white balls, 4 red balls and 5 black balls.
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If three squares are selected at random from chessboard, then the probability that they form the letter 'L' is
An unbiased dice, with faces numbered 1, 2, 3, 4, 5, 6, is thrown n times and the list of n numbers shown up is noted. Then find the probability that among the numbers 1, 2, 3, 4, 5, 6 only three numbers appear in this list and each number appears at least once.
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are
Two integers are chosen at random and multiplied. Find the probability that the product is an even integar.
Three randomly chosen non-negative integers x, y and z are found to satisfy the equation x + y + z 10. Then the probability that z is even, is
The probability that a random chosen three-digit number has exactly 3 factors is
Consider f(x)=x3+ax2+bx+c. Parameters a, b, c are chosen, respectively, by throwing a die three times. Then the probability that f(x) is an increasing function is
Fourteen numbered balls (1, 2, 3, …, 14) are divided in 3 groups randomly. Find the probability that the sum of the numbers on the balls, in each group, is odd.