class 12

Math

Algebra

Probability I

There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

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.

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 $0.23≤P(B∩C)≤0.48$.

Two natural numbers x and y are chosen at random. What is the probability that $x_{2}+y_{2}$ is divisible by 5?

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

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

Box 1 contains three cards bearing numbers, 1, 2, 3, box 2 contains five cards bearing number 1, 2, 3, 4, 5, and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let $x_{i}$ be the number on the card drawn from the $i_{th}$ box, i = 1, 2, 3. The probability that $x_{1}+x_{2}+x_{3}$ is odd, is

If the probability of a six-digit number N whose six digits are 1, 2, 3, 4, 5, 6 written as random order is divisible by 6 is p, then the value of $1/p$ is _______.

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 ?