EXAMPLES ON PROBABILITY

1. Ms. NEHA CHANDRAKANT PATIL
Assistant Professor ( Department of Mathematics)
Changu KanaThakur ACS College, New Panvel

2. 1) Write the sample space for rolling a die.
• S = { 1,2,3,4,5,6}
n(S)= 6
2) Write the sample space for rolling two dice.
• S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4) (2,5),(2,6),
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6), (4,1),(4,2),(4,3) ,(4,4),(4,5) , (4,6),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6), (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }
n(S) = 36

3. 3) In a bag, there are 5 red balls and 7 black balls. What is
the probability of getting a black ball?
• The number of red balls = 7 The number of black balls = 7
Therefore, total number of balls in a bag = 12
Probability of getting a black ball =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑎𝑐𝑘 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
=
7
12

4. 4)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?
• The number of red balls = 8 The number of blue balls = 7
The number of green balls = 6
Therefore, total number of balls in a box = 21
Ball is neither red nor green = blue ball
Probability of getting a blue ball =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑢𝑒 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
=
7
21
=
1
3

5. 5) There are 5 green, 7 red balls. Two balls are selected one by one
without replacement. Find the probability that first is red and second is
green.
• The number of red balls = 5 The number of green balls = 7
Therefore, total number of balls in a box = 12
Probability of getting a red ball =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
=
5
12
Probability of getting a green ball =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑒𝑒𝑛 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑎𝑙𝑙𝑠 𝑖𝑛 𝑎 𝑏𝑎𝑔
=
7
11
By multiplication rule, probability that first is red and second is green =
5
12
*
7
11
=
35
132

6. 6) Find the probability that a leap year has 52 Sundays.
• A leap year can have 52 Sundays or 53 Sundays.
In a leap year, there are 366 days out of which there are 52 complete weeks
& remaining 2 days.
Now, these two days can be (Sat, Sun) (Sun, Mon) (Mon, Tue) (Tue, Wed)
(Wed, Thur) (Thur, Friday) (Friday, Sat).
So there are total 7 cases out of which (Sat, Sun) (Sun, Mon) are two
favorable cases.
So, P (53 Sundays) = 2 / 7
Now, P(52 Sundays) + P(53 Sundays) = 1
So, P (52 Sundays) = 1 - P(53 Sundays) = 1 – (2/7) = (5/7)

7. 7) 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?
• Here, S = {1,2,3, 4, 5, 6, 7, 8……., 20}
n(S) = 20
Let A be the event of getting a number which is a multiple of 3 or 5
Therefore, A = {3,6,9,12,15,18,5, 10, 20}
n(A) =9
Probability that the ticket drawn has a number which is a multiple of 3 or 5 =
𝑛(𝐴)
𝑛(𝑆)
=
9
20

8. 8) In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at
random. What is the probability of getting a prize?
• Here, sample space = ( prizes + blanks ) = 35
Probability of getting a prize =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑟𝑖𝑧𝑒𝑠
𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒
=
10
35
=
2
7

9. 9) A bag contains 6 black and 8 white balls. One ball is drawn at
random. What is the probability that the ball drawn is white?
• Number of black balls = 6
• Number of white balls = 8
therefore, total number of balls = 14
Probability that the ball drawn is white =
8
14
=
4
7

10. 10) Out of 300 students in a school, 95 play cricket only, 120
play football only, 80 play volleyball only and 5 play no games.
If one student is chosen at random, find the probability that
(i) he plays volleyball
(ii) he plays either cricket or volleyball
(iii) he plays neither football nor volleyball.
• Total number of students = 300
Number of students play cricket = 95
Number of students play football = 120.
Number of students play volleyball = 80.
Number of student who plays no games = 5.

11. i) Therefore, the probability of getting a player who plays
volleyball
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 students play volleyball
𝑡𝑜𝑡𝑎𝑙 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
=
80
300
ii) The probability of getting a player who plays either cricket or
volleyball =
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 students play cricket or volleyball
𝑡𝑜𝑡𝑎𝑙 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
=
95
300
+
80
300
=
95+80
300
=
175
300
=
7
12

12. • The probability of getting a player who plays neither football nor
volleyball
= probability of getting a player who plays cricket or no games at
all
=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 students play cricket or no game
𝑡𝑜𝑡𝑎𝑙 𝑠𝑡𝑢𝑑𝑒𝑛𝑡𝑠
=
95
300
+
5
300
=
95+5
300
=
100
300
=
1
3