class 12

Math

Algebra

Probability I

A bag contains 4 red and 6 blach balls O balls is drawn at random from the bag, its colour is observed and this ball along with two addibonal balls of the same colour are returnted to the bag, then the probabilaty then the drawn ball is red, is

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A bag contains 12 pairs of socks. Four socks are picked up at random. Find the probability that there is at least one pair.

Let A, B, C be three events such that P(A) = 0.3, P(B) = 0.4, P(C ) = 0.8, $P(A∩B)$ = 0.08, $P(A∩C)$ = 0.28, $P(A∩B∩C)=0.09$. If $P(A∪B∪C)≥0.75$, then show that $0.23≤P(B∩C)≤0.48$.

A dice is rolled three times, find the probability of getting a larger number than the previous number each time.

Five persons entered the lift cabin on the ground floor of an eight-floor house. Suppose that each of them, independently and with equal probability, can leave the cabin at any floor beginning with the first. Find out the probability of all five persons leaving at different floors.

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, then find the probability that it is rusted or is a nail.

A five-digit number is formed by the digit 1, 2, 3, 4, 5 without repetition. Find the probability that the number formed is divisible by 4.

If the squares of a $8×8$ chessboard are painted either red or black at random. The probability that the chessboard contains equal number of red and black squares is

Five different games are to be distributed among four children randomly. The probability that each child get at least one game is p, then the value of $[1/p]$ is, where [ . ] represents the greatest integer function, _______.