# Probability

## Probability

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Question 1 |

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

1/2 | |

2/5 | |

8/15 | |

9/20 |

Question 1 Explanation:

Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5 = {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E) =(n(E)/n(S)) ==>9/20

Question 2 |

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?
.

1/3 | |

3/4 | |

7/19 | |

8/21 |

Question 2 Explanation:

Total number of balls = (8 + 7 + 6) = 21.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 7.
P(E) = (n(E)/n(S)) ==>7/21 ==>1/3 .

Question 3 |

What is the probability of getting a sum 9 from two throws of a dice?

1/6 | |

1/8 | |

1/9 | |

1/12 |

Question 3 Explanation:

In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) = (n(E)/n(S)) ==>4/36 ==>1/9 .

Question 4 |

Three unbiased coins are tossed. What is the probability of getting at most two heads?

3/4 | |

1/4 | |

3/8 | |

7/8 |

Question 4 Explanation:

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E) = (n(E)/n(S)) ==>7/8

Question 5 |

Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?

1/2 | |

3/4 | |

3/8 | |

5/16 |

Question 5 Explanation:

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.
Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),
(3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),
(6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E) = 27.
P(E) =(n(E)/n(S)) ==>27/36 ==>3/4

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