Class 12

Math

Algebra

Probability I

A card is drawn at random from a well-shuffled pack of 52 cards. Find theprobability that it is neither a ace nor a king.

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A and B toss a fair coin each simultaneously 50 times. The probability that both of them will not get tail at the same toss is

If a coin is tossed n times, then find the probability that the head appears odd number of times.

Two numbers a and b chosen at random from the set of first 30 natural numbers. Find the probability that $a_{2}−b_{2}$ is divisible by 3.

Five different digits from the set of numbers {1, 2, 3, 4, 5, 6, 7} are written in random order. Find the probability that five-digit number thus formed is divisible by 9.

A mapping is selected at random from the set of all the mappings of the set A = {1, 2, …, n} into itself. Find the probability that the mapping selected is an injection.

A and B are two candidates seeking admission to IIT. The probability that A is selected is 0.5 and the probability that A and B are selected is at most 0.3. Is it possible that the probability of B getting selected is 0.9?

Three numbers are chosen at random without replacement from {1, 2, 3, …, 10}. Find the probability that the smallest of the chosen numbers is 3, or the greatest one is 7.

A cricket club has 15 members, of whom only 5 can bowl. If the names of 15 members are put into a box and 11 are drawn at random, then the probability of getting an eleven containing at least 3 bowlers is