Important for :

1

C

The total number of students = 18When 1 name was selected from 18 names, the probability that he was of section B

= | 6 | = | 1 |

18 | 3 |

But from the question, there are 6 students from the section B and the age of all 6 are different therefore, the probability of selecting one i.e. youngest student from 6 students will be 1/6

Hence, option C is correct.

2

A

Let, the number of pink balls be pProbability of choosing a pink ball = | p |

35 |

=> | 3 | = | p |

7 | 35 |

=> p = 15

So, remaining number of balls = (35 – 15) = 20

Number of orange balls = | 2 | × 20 = 2 × 4 = 8 |

2 + 3 |

Therefore, reqd. probability = |
^{8}C_{1} × ^{15}C_{1} |

^{35}C_{2} |

= | 8 × 15 | = | 24 |

35 × 34/2 | 119 |

Hence, option A is correct.

3

D

Number of ways in which the person can pick three balls out of 18 balls = Number of ways of picking 3 balls of same colour =

Probability of picking three balls of same color

= | 80 | = | 5 |

816 | 51 |

Required probability = 1 – probability of picking three balls of same colour

= 1 – | 5 | = | 46 |

51 | 51 |

Hence, option D is correct.

4

B

Total boxes = 16Total pieces = 16

Similar pieces = 8 pawns, 2 bishops, 2 rooks, 2 knights

Total ways of arranging these 16 pieces in 16 boxes

= | 16! | = | 16! |

(8! 2! 2! 2!) | (8 × 8!) |

Ways of correct arrangement = 1

Probability of correct arrangement = | 1 |

(16! / (8 × 8!) |

= | (8 × 8!) | = | 8! |

16! | (2 × 15!) |

Hence, option B is correct..

5

D

We fix the red face and to its left pink face and bottom face as blue

The number of ways to arrange the other three colors = 3!

Total ways of painting the six colors

First we fix any one color on any one face, let’s say red color.

The number of ways five color can be painted = 5!

Eliminating the repeated possibilities = | 5! | = 5 × 3! |

4 |

We divide by four to eliminate the repeated possibilities as shown in the figure below. These possibilities are counted as different but don’t give us a different arrangement. The arrangement in all four is same.

Probability (Red, pink and blue share a common corner)

= | 3! | = | 1 |

5 × 3! | 5 |

Hence, option D is correct.

Probability is a fundamental concept in math and statistics and deals with the likelihood of an event to occur.

It can range from 0 to 1, where 0 means impossible to occur and 1 indicates a certain event. The probability theory is aimed to find out about how likely events will happen.

To get a grasp over the topic, you can practice daily questions at Smartkeeda. This will help you get better at a topic and improve your time management skills.

The explanation provided at Smartkeeda is in-depth and will help you learn all the essentials of Probability. This is often a dreaded section, but with regular practice, you will be able to solve the questions.

If you have any feedback/ queries/ suggestions for us, please drop your message in the comment section.

Regards

**Team Smartkeeda**

It can range from 0 to 1, where 0 means impossible to occur and 1 indicates a certain event. The probability theory is aimed to find out about how likely events will happen.

To get a grasp over the topic, you can practice daily questions at Smartkeeda. This will help you get better at a topic and improve your time management skills.

The explanation provided at Smartkeeda is in-depth and will help you learn all the essentials of Probability. This is often a dreaded section, but with regular practice, you will be able to solve the questions.

If you have any feedback/ queries/ suggestions for us, please drop your message in the comment section.

Regards