Home
Class 11
MATHS
A bag contain 8 red and 5 white balls. T...

A bag contain 8 red and 5 white balls. Three balls are drawn at random. Find the probability that: All the three balls are white. All the three balls are red. One ball is red and two balls are white.

Text Solution

Verified by Experts

`therefore"Number of red balls "=8`
`"and number of white balls "5`
(i) `"P(all the three balls are white) "=(.^(5)C_(3))/(.^(13)C_(3))=((5!)/(3!2!))/((13!)/(3!10!)) = (5!)/(3!2!) xx (3!10!)/(13!)`
`=(5xx4xx3xx2!)/(2!)xx(10!)/(13xx12xx11xx10!)=(5xx4xx3)/(13xx12xx11)`
`=(5)/(13xx11)=(5)/(143)`
`(5xx4xx3)/(13xx12xx11)=(5)/(13xx11)=(5)/(143)`
(ii) `"P(all the three balls are red) " =(.^(8)C_(3))/(.^(13)C_(3))=(8!)/((315!)/((13!)/(3!10!)))=(8!)/(3!xx5!)xx(3!10!)/(13!)`
`=(8xx7xx6xx5!)/(5!)xx(10!)/(13xx12xx11xx10!)`
`=(8xx7xx6)/(13xx12xx11)=(28)/(143)`
(iii) `"P(one ball is red and two balls are white)" =(.^(8)C_(1))/(.^(13)C_(3))=(8xx10)/(13xx6xx11)=(40)/(143)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    NCERT EXEMPLAR|Exercise Objective Type Questions|12 Videos

  • PROBABILITY

    NCERT EXEMPLAR|Exercise True/False|7 Videos

  • PROBABILITY

    NCERT EXEMPLAR|Exercise Matching The Columns|2 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    NCERT EXEMPLAR|Exercise OBJECTIVE TYPE QUESTIONS|5 Videos

  • RELATIONS AND FUNCTIONS

    NCERT EXEMPLAR|Exercise True /False|5 Videos

Similar Questions

Explore conceptually related problems

A bag contain 8 red and 5 white balls.Three balls are drawn at random.Find the probability that: (i) All the three balls are white.(ii) All the three balls are red.(iii)One ball is red and two balls are white.

A bag contains 7 red and 3 white balls. Three balls are drawn at random. Probability, that the two balls are red and one is white, is

A bag contains 9 red and 12 white balls. One ball is drawn at random. Find the probability that the ball drawn is red.

An urn contains 8 red and 5 white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn, is

A bag contains 6 white,4 red and 9 black balls.If three balls are drawn at random,find the pobability that two of the balls drawn are white

There are 5 white and 4 red balls in a bag. Two balls are drawn at random. Find the probability that both balls are white.

A bag contains 8 red, 2 black and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is not black?

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