class 11

Math

Algebra

Probability I

Three boys and two girls stand in a queue. The probability, that the number of boys ahead is at least one more than the number of girls ahead of her, is (A) $21 $ (B) $31 $ (C) $32 $ (D) $43 $

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A local post office is to send M telegrams which are distributed at random over N communication channels, $(N>M)$. Each to telegram is sent over any channel with equal probability. Chance that not more than one telegram will be sent over each channel is

The number 1, 2, 3, …, n are arrange in a random order. The probability that the digits 1, 2, 3,…, $k(k<n)$ appear as neighbors in that order is

An ordinary cube has four blank faces, one face marked 2 and one face marked 3. Then find the probability of obtaining a total of exactly 12 in 5 throws.

Three distinct numbers a, b and c are chosen at random from the numbers 1, 2, …, 100. The probability that $List Ia. a, b, c are in AP isb. a, b, c are in GP isc.a1 .b1 .c1 are in GP isd. a + b + c is divisible by 2 is List IIp.16170053 q.661 r.221 s.21 $

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 box contains two 50-paise coins, five 25-paise coin and a certain fixed number $N(≥2)$ of 10 and 5-paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these 5 coins is less than 1 rupee and 50 paise.

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back ? How many seating arrangements are possible if 3 girls should sit together in a back row on adjacent seats? Now, if all the seating arrangements are equally likely, what is the probability of 3 girls sitting together in a back row on adjacent seats ?

If out of 20 consecutive whole numbers two are chosen at random, then find the probability that their sum is odd.