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1. 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?

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Solution:
Here, S = {1, 2, 3, 4, ...., 19, 20}
Let E = event of getting a multiple of 3 or 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 20}
∴P(E)=n(E)n(S)=920
2. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Discuss
Solution:
Total number of balls
= (2 + 3 + 2)
= 7
Let S be the sample space
Then, n(S) = Number of ways of drawing 2 balls out of 7
n(S)=7C2n(S)=(7×6)(2×1)n(S)=21
Let E = Event of 2 balls, none of which is blue
∴ n(E) = Number of ways of drawing 2 balls out of (2 + 3) balls
n(E)=5C2n(E)=(5×4)(2×1)n(E)=10∴P(E)=n(E)n(S)=1021
3. 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?

Discuss
Solution:
Total number of balls
= (8 + 7 + 6)
= 21
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue
∴n(E)=7∴P(E)=n(E)n(S)=721=13
4. What is the probability of getting a sum 9 from two throws of a dice?

Discuss
Solution:
In two throws of a dice, n(S) = (6 x 6) = 36
Let E = event of getting a sum
= {(3, 6), (4, 5), (5, 4), (6, 3)}
∴P(E)=n(E)n(S)=436=19
5. Three unbiased coins are tossed. What is the probability of getting at most two heads?

Discuss
Solution:
Getting at most Two heads means 0 to 2 but not more than 2
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}
∴P(E)=n(E)n(S)=78
6. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

Discuss
Solution:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36

Then, E = {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
∴n(E)=27∴P(E)=n(E)n(S)=2736=34
7. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

Discuss
Solution:
Let S be the sample space and E be the event of selecting 1 girl and 2 boys
Then, n(S) = Number ways of selecting 3 students out of 25
=25C3=25×24×233×2×1=2300n(E)=10C1×15C2=10×15×142×1=1050∴P(E)=n(E)n(S)=10502300=2146
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?

Discuss
Solution:
P(gettingaprize)=1010+25=1035=27
9. From a pack of 52 cards, two cards are drawn together at random. What is the probability of both the cards being kings?

Discuss
Solution:
Let S be the sample space
Then,n(S)=52C2=52×51(2×1)=1326
Let E = event of getting 2 kings out of 4
∴n(E)=4C2=4×32×1=6∴P(E)=n(E)n(S)=61326=1221
10. Two dice are tossed. The probability that the total score is a prime number is:

Discuss
Solution:
Clearly, n(S) = (6 x 6) = 36
Let E = Event that the sum is a prime number.Then
E = {(1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5)}
∴n(E)=15∴P(E)=n(E)n(S)=1536=512

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