# Drawing/Picking/Choosing Single/One ball from a bag/urn/box - Probability - Problems Solutions

# Problem 1

If a ball is drawn at random, from a bag containing 5 white and 3 black balls, then write the number of successes and failures for the ball to be a black one.

# Solution

Total number of balls in the bag

= 5 White + 3 Black

= 8

**Experiment** :

Drawing a ball from a bag containing 5 white and 3 black balls

Total Number of Possible Choices

= Number of ways in which one ball can be drawn from the total 8

⇒ n | = | ^{8}C_{1} | ||

= |
| |||

= | 8 |

Let

**A** : the event of the ball drawn being black

## For Event A

Favorable (Black) | Unfavorable (Others) | Total | |
---|---|---|---|

Available | 3 | 5 | 8 |

To Choose | 1 | 0 | 1 |

Choices | ^{3}C_{1} | ^{5}C_{0} | ^{8}C_{1} |

Number of successes for the event of drawing a black ball

⇒ Number of Favorable Choices for event A

= Number of ways in which one black ball can be drawn from the total 3

⇒ m_{A} | = | ^{3}C_{1} | ||

= |
| |||

= | 3 |

Number of failures for the event of drawing a black ball

⇒ Number of Unfavorable Choices for event A

= Total Number of possible choices − Number of Favorable choices

⇒ m_{Ac} | = | n − m_{A} |

= | 8 − 3 | |

= | 5 |

# Problem 2

If a ball is drawn at random from a bag containing 12 black and 15 white balls, what is the probability and odds that it is a) Black b) White?

# Problem 3

A bag contains 3 red balls, 4 white balls and 7 black balls the probability of drawing a red or a black ball is

Solution Ans :

5 |

7 |

# Problem 4

A ball is drawn at random from a box containing 16 red balls, 24 white balls and 15 blue balls. Determine the probability that it is (i) Not red, (ii) Red or white, (iii) Neither Red Nor Blue

# Problem 5

Define the Event and identify the number of favourable choices in the following cases which relate to the experiment of drawing a ball

- Drawing a ball which is not blue from a box containing 24 balls of the same shape and weight of which 8 are green, 6 are red and the rest are blue.
- Drawing a ball which is neither a black ball nor a green ball from a bag containing 4 green, 5 black, 6 white balls.
- Choosing a ball which is either red or blue from a bag containing 18 white, 16 green, 14 blue and 12 red balls.

Solution Ans : i) 14, ii) 6, iii) 26

# Practice Problems

- A ball is drawn at random from an urn containing 15 green, 25 black, 16 white balls. . The probability that it is either a black ball or a green ball is
- A box contains 150 bolts of which 50 are defective. Find the probability that the bolt chosen at random from the box is not defective.
- An urn contains 9 red, 7 white and 4 black balls. A ball is drawn at random. What is the probability that the ball drawn will be (i) Red or Black, (ii) White or Black, (iii) Not red, (iv) Neither Red nor Black

Author : The Edifier