Home
Class 12
MATHS
Box 1 contains three cards bearing numbe...

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 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 ith box, i = 1, 2, 3. The probability that `x_1+x_2+x_3` is odd is The probability that `x_1, x_2, x_3` are in an aritmetic progression is

A

`(9)/(105)`

B

`(10)/(105)`

C

`(11)/(105)`

D

`(7)/(105)`

Text Solution

Verified by Experts

Here, `2x_(2) = x_(1) + x_(3)`
`implies x_(1) + x_(3)` = even
So, either `x_(1)` and `x_(3)` are both odd or both even.
Hence, number of favorable ways = `.^(2)C_(1).^(4)C_(1) + .^(1)C_(1) .^(3)C_(1) = 11`.
Therefore, required probability is `(11)/(105)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 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 ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 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 ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 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 ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 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 ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 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 ith box, i = 1, 2, 3. The probability that x_1, x_2, x_3 are in an aritmetic progression is

Box 1 contains three cards bearing numbers 1, 2,3, box 2 contains five cards bearing numbers 1,2,3,4,5, and box 3 contains seven card bearing numbers 1,2,3,4,5,6,7. Acard 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-

Box 1 contains three cards bearing numbers 1, 2,3, box 2 contains five cards bearing numbers 1,2,3,4,5, and box 3 contains seven card bearing numbers 1,2,3,4,5,6,7. Acard 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) are in an arithmetic progression, is-

A box contains cards numbered 3, 5, 7, 9, ....., 35, 37. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.

A box contains cards numbered from 13, 14, 15, ....., 60. A card is drawn at random from the box. Find the probability that the number on the drawn card is divisible by 2 or 3

A box contains cards numbered from 13, 14, 15, ....., 60. A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number