Drawing/Picking/Choosing/Selecting a Numbered Card from a Pack/Box/Urn - Probability - Problems Solutions

Problem 1

Determine the probability that a digit chosen at random from the digits 1, 2, 3, ... , 9 will be a) odd b) even c) a multiple of 3
Solution Ans : a)
5
9
, b)
4
9
, c)
1
3

Problem 2

A card is drawn from a pack of 52 cards numbered 2 to 53. the probability and odds that the number on the card is a prime number less than 20 is
Solution Ans :
2
13
, 2 : 11, 11 : 2

Problem 3

One hundred tickets are numbered as 00, 01, 02, ... , 09, 10, 11, ... , 99. If one ticket is drawn at random from them and if A is the event of getting 9 as the sum of the numbers on the tickets and B the event of the product of the numbers on the card being 0, then P(A) = ? and P(B) = ?
Solution Ans :
1
10
,
19
100

Problem 4

If one ticket is drawn at random from a bag containing 20 tickets numbered 1 to 20 the probability that it is a multiple of 5 or 7 is
Solution Ans :
3
10

Problem 5

An urn contains 13 balls numbered from 1 to 25. Find the probability that a ball selected at random is a ball with a number that is a multiple of 3 or 4.
Solution Ans :
12
25

Problem 6

An integer is chosen at random from the first hundred positive integers. The probability that the integer chosen is divisible by 6 and 8 is ?
Solution Ans :
2
25

Problem 7

Each of the two digit numbers than can be formed from the integers 1 to 9 no digit repeated, is written on a card. Then all the cards are thoroughly shuffled and stacked. If one card is drawn from the stack, find the probability that the sum of the digits in the number on it will be 10.
Solution Ans :
1
9

Problem 8

A number x is chosen at random out of the natural numbers 1, 2, 3,... 100. Find the probability for x to follow x +
100
x
> 50
Solution Ans :
14
25

Problem 9

Define the Event and identify the number of favourable choices in the following cases:
  1. Drawing a card with a number which is a square marked on it from a packet of 100 cards numbered 1 to 100.
  2. Choosing a number at random from among the first 120 natural numbers which is a multiple of 5 or 15
  3. Drawing a card with a number that is divisible by 3 or 7 from a set of 17 cards numbered 1, 2, 3, ... , 17.
  4. Choosing a random a number that is divisible by 6 or 8 from among 1 to 90
  5. Getting a number between 5 and 55 (both inclusive) which is divisible by 1 and itself only is ...
Solution Ans : 1) 10, 2) 24, 3) 5, 4) 23, 5) 13

Practice Problems

  1. The probability that a number selected at random from the set of numbers {1, 2, 3, ..., 100} is a cube is ...

  2. A card is drawn from pack of 1000 cards numbered 1 to 1000. Find the probability of drawing a number divisible by 13.

  3. If a number is selected at random from the natural numbers 1 to 10, then find the probability for the number to be (a) a prime number (b) a perfect square.

  4. A bag contains 20 tickets with marked numbers 1 to 20. One ticket is drawn at random. Find the probability that it will be a multiple of (i) 2 or 5 (ii) 3 or 5

  5. A number x is chosen at random out of the natural numbers 1, 2, 3,... 100. Find the probability for x to follow x +
    100
    x
    > 29

  6. Define the Event and identify the number of favourable choices in the following cases:

    1. Choosing an integer which is divisible by 6 or 8 from the first two hundred positive integers
    2. Picking a ticket marked with a multiple of 2 or 3 on drawing a ticket from 20 tickets marked 1,2,3 ... 20
Author : The Edifier
Page PS7