Home
Class 12
MATHS
If the squares of a 8 xx 8 chess board ...

If the squares of a `8 xx 8` chess board are painted either red and black at random .The probability that not all squares is any alternating in colour is

A

`(1 - 1//2^(7))^(8)`

B

`1//2^(56)`

C

`1 - 1//2^(7)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
The total number of ways of painting first column when colors are not alternating is `2^(8) - 2`. The total number of ways when no column has alternating colors is `(2^(8) - 2)^(8)//2^(24)`.
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE|Exercise Exercise (Matrix)|2 Videos

  • PROBABILITY I

    CENGAGE|Exercise Exercise (Numerical)|7 Videos

  • PROBABILITY I

    CENGAGE|Exercise Exercise (Multiple)|8 Videos

  • PROBABILITY AND STATISTICS

    CENGAGE|Exercise Question Bank|24 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

Similar Questions

Explore conceptually related problems

An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. The probability that the second ball drawn is red will be

An urn contains 10 red and 8 white balls. One ball is drawn at random. Find the probability that the ball drawn is white .

An urn contains 5 red and 5 black balls. A balls is drawn at random , its colour is noted and is returned to the urn. Moreover , 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random . Then probability that the second ball drawn is red will be .......

A bag contains 7 red and 4 black balls, 3 balls drawn at random. Find the probability that (i) all are red (ii) one red and 2 black.

A box contains 2 black, 4 white, and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn front the box. The probability that the balls drawn are in the sequence of 2 black, 4 white, and 3 red is a. 1//1260 b. 1//7560 c. 1//126 d. none of these

The number of all possible squares in a chess board is