class 12

Math

Algebra

Probability I

Three randomly chosen nonnegative integers $x,yandz$are found to satisfy the equation $x+y+z=10.$Then the probability that $z$is even, is:$125 $ (b) $21 $ (c) $116 $ (d) $5536 $

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Let $AandB$ be two event such that $P(A∪B)≥3/4$ and $1/8≤P(A∩B)≤3/8.$ Statement 1: $P(A)+P(B)≥7/8.$ Statement 2:$P(A)+P(B)≤11/8.$

A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is $1/4$ b. $1/3$ c. $2/3$ d. none of these

Six boys and six girls sit in a row randomly. Find the probability that (i) the six girls sit together, (ii) the boys and girls sit alternately.

Five different games are to be distributed among 4 children randomly. The probability that each child get at least one game is a. $1/4$ b. $15/64$ c. $5/9$ d. $7/12$

Cards are drawn one at random from a well shuffled full pack of 52 playing cards until 2 aces are obtained for the first time. If $N$ is the number of cards required to the drawn, then show that $P,{N=n}=50×49×17×13(n−1)(52−n)(51−n) ,where2<n<50$

A drawer contains a mixture of red socks and blue socks, at most 17 in all. It so happens that when two socks are selected randomly without replacement, there is a probability of exactly 1/2 that both are red or blue. The largest possible number of red socks in the drawer that is consistent with this data is _______.

A bag contains 3 red, 7 white, and 4 black balls. If three balls are drawn from the bag, then find the probability that all of them are of the same color.

Find the probability of getting total of 5 or 6 in a single throw of two dice.