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1. Probability

2. • Favorable events + Unfavorable events = Total number of
Events
• Probability of event =
• Maximum value of Favorable Events = Total events =
max(P(E))= 1
• Minimum value of Favorable Events = min(P(E)) = 0
• 0 < P(E) < 1
Basics :

3. 1. From a set of 1st 20 natural numbers, if one number is selected at a time,
what is the probability that it is a multiple of 3 or 5?
2. When 2 dice are rolled at a time, what is the probability that sum of the
numbers on the dice is at least 10?
3. When 5 unbiased coins are tossed, what is the probability that they get
exactly 3 heads?
4. From a pack of 52 cards, if one card is selected at a time, what is the
probability that it is a diamond or a face card?
5. What is the probability that a non leap year has 53 Monday’s?
6. A bag contains 3 red, 4 blue and 5 green colored balls. If 2 balls are
selected at a time, what is the probability that both the balls are of
different colors?

4. 1. From a set of 1st 20 natural numbers, if one number is selected
at a time, what is the probability that it is a multiple of 3 or 5?
Ans :
divisible by 3 are 3,6,….18 => 6 numbers
divisible by 5 are 5,10,….20 => 4 numbers
15 is common for both .
 Total number of favorable events are 10 – 1= 9
 Total number of events are 20
Probability that it is multiple of 3 or 5 = .
Probability that it is multiple of 3 or 5 =

5. When 2 dice are rolled at a time, what is the probability that sum of the
numbers on the dice is at least 10?
2.
NOTE :
When n dice are rolled at a time, then total number of events is given by
For the sum to be 10, then pair should be (4,6) (5,5)
 Total number of favorable events are 2
 Total number of events are 36
Probability that the sum is 10 =
Ans :
Probability that the sum is 10

6. When 5 unbiased coins are tossed, what is the probability that they
get exactly 3 heads?
3.
Ans :
NOTE :
When ‘n’ biased coins are tossed at a time, then total number of events is given by
To get exactly 3 heads, the pairs should be HHHTT i.e. taking 3 coins with heads
 Total number of favorable events are
 Total number of events are
Probability to get exactly 3 heads =
Probability to get exactly 3 heads =

7. 52
26 BLACK 26 WHITE
13 SPADES 13 HEART13 CLUBS 13 DIAMOND
A,1…..Q,K A,1…..Q,K A,1…..Q,K A,1…..Q,K

8. From a pack of 52 cards, if one card is selected at a time,
what is the probability that 1) it is a red card?
2) it is a spade
3) it is a Ace
4) it is a diamond king
5) it is a face card
6) it is a king or queen
7) it is a queen or heart
4.

9. 1. probability that it is a red card =
2. probability that it is a Spade =
3. probability that it is a red card =
4. probability that it is a red card =
5. probability that it is a red card = =
6. probability that it is a red card = =
7. probability that it is a red card = =
Ans :

10. What is the probability that a non leap year has 53 Monday’s?5.
Ans :
365 days = 52 weeks + 1 day
That extra one day can be Monday or Tuesday …. Or Sunday.
=> Considering the case of 52 Monday’s + the extra one day should be
Monday
 probability that a non leap year has 53 Monday’s =
Probability that a non leap year has 53 Monday’s =

11. A bag contains 3 red, 4 blue and 5 green colored balls. If 2 balls are
selected at a time, what is the probability that both the balls are of
different colors?
6.
Ans :
Probability that both balls are of different colors =
3 – R , 4 – B , 5 – G
Probability that both balls are of different colors =
=

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Continued…..
Problems for practice are given in the description of the video.

13. Practice problems
on Probability

14. 1. From a set of 1st 10 natural numbers, if 2 numbers are selected at a
time, what is the probability that the sum is 10?
2. From a set of 1st 40 natural numbers, if one number is selected at a
time, what is the probability that it is a multiple of 7?
3. What is the probability that a non leap year has 52 Monday’s?
4. From a pack of 52 cards, if one card is selected at a time, what is
the probability that it is a diamond or a face card(J,K,Q)?

15. 1. From a set of 1st 10 natural numbers, if 2 numbers are selected
at a time, what is the probability that the sum is 10?
Ans :
Numbers that sum is 10 are (1,9) (2,8) (3,7) (4,6)
 Total number of favorable events are 4
 Total number of events are 45
Probability that sum is 10 =
Probability that sum is 10 =

16. From a set of 1st 40 natural numbers, if one number is selected at a
time, what is the probability that it is a multiple of 7?
Ans :
7,14,21,28,35,42
 Total number of favorable events are 5
 Total number of events are 40
Probability that it is multiple of 7 = .
Probability that it is multiple of 7 =
2.

17. What is the probability that a non leap year has 52 Monday’s?3.
Ans :
365 days = 52 weeks + 1 day
That extra one day can be Monday or Tuesday …. Or Sunday.
=> Considering the case of 52 Monday’s + the extra one day should be
Monday
 probability that a non leap year has 52 Monday’s =
Probability that a non leap year has 53 Monday’s =

18. From a pack of 52 cards, if one card is selected at a time, what is the
probability that it is a diamond or a face card(J,K,Q)?
4.
Ans :
Total number of favorable events are
13 + 12 =25
Total number of events are 52
probability that it is a diamond or a face card = .
Probability that it is a diamond or a face card = .

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