# NCERT Class 11 Mathematics Solutions: Chapter 16 – Probability Miscellaneous Exercise Part 4 (For CBSE, ICSE, IAS, NET, NRA 2023)

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1. From the employees of a company, persons are selected to represent them in the managing committee of the company. Particulars of five persons are as follows:

 S. No Name Sex Age in years Harish Rohan Sheetal Alis Salim

A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over years?

Consider be the event in which the spokesperson will be a male and be the event in which the spokesperson will be over years of age.

Accordingly,

Since there is only one male who is over years of age,

We know that:

The probability that the spokesperson will either be a male or over years of age is .

2. If -digit numbers greater than are randomly formed from the digits , what is the probability of forming a number divisible by when,

(i) the digits are repeated?

(ii) the repetition of digits is not allowed?

When the digits are repeated

Since four-digit numbers greater than are formed, the leftmost digit is either or .

The remaining places can be filled by any of the digits as repetition of digits is allowed.

Total number of 4-digit numbers greater than

[In this case, cannot be counted; so is subtracted]

A number is divisible by if the digit at its units place is either .

Total number of 4-digit numbers greater than that are divisible by

The probability of forming a number divisible by when the digits are repeated is

When repetition of digits is not allowed

The thousands place can be filled with either of the two digits .

The remaining places can be filled with any of the remaining digits.

Total number of 4-digit numbers greater than

When the digit at the thousands place is , the units place can be filled only with and the tens and hundreds places can be filled with any two of the remaining 3 digits.

Number of -digit numbers starting with and divisible by

When the digit at the thousands place is , the units place can be filled in two ways and the tens and hundreds places can be filled with any two of the remaining 3 digits.

Number of -digit numbers starting with and divisible by

Total number of -digit numbers greater than that are divisible by 5

The probability of forming a number divisible by when the repetition of digits is not allowed is