Class 9 Maths: Probability – Practice Extra Questions

Ans: B

Explanation: Each coin has two possible outcomes: Heads (H) or Tails (T). When three coins are tossed together, the total number of outcomes is 2 * 2 * 2 = 8.
Correct Option: B

Ans: D

Solution:
The probability of selecting a green marble is the number of green marbles divided by the total number of marbles.
Total marbles = 7 (blue) + 9 (green) = 16
Probability (Green) = 9/16
Answer: 9/16

Ans: A

Solution: There are 13 hearts in a standard deck of 52 cards. The probability of drawing a heart is the number of hearts divided by the total number of cards.
Answer: $\frac{13}{52} = \frac{1}{4}$

Ans: D

Explanation: The probability of scoring a boundary is 6/30. The probability of not scoring a boundary is the complement of scoring a boundary. Therefore, we subtract the probability of scoring a boundary from 1.

Correct Answer: 24/30

Ans: D

The possible outcomes are the numbers 1 to 8. The factors of 8 are 1, 2, 4, and 8. There are 8 possible outcomes in total, and 4 favorable outcomes. The probability is $\frac{4}{8} = \frac{1}{2}$.

Ans: D

Solution: There are 6 x 6 = 36 possible outcomes. The combinations that sum to 8 are (2,6), (3,5), (4,4), (5,3), (6,2). There are 5 such combinations.
Answer: 5/36

Ans: C

Solution:
Numbers greater than 4 are 5 and 6.
Frequency of 5 = 95
Frequency of 6 = 100
Total frequency of numbers greater than 4 = 95 + 100 = 195
Total number of rolls = 600
Experimental probability = (Frequency of numbers greater than 4) / (Total number of rolls) = 195/600 = 13/40

Answer: 13/40

Ans: D

Explanation: Let ‘g’ be the number of green marbles and ‘b’ be the number of blue marbles. We know that g + b = 24. The probability of picking a green marble is g/24, and we’re given that this probability is 2/3. So, g/24 = 2/3. To solve for ‘g’, multiply both sides by 24: g = (2/3) * 24 = 16. Since there are 16 green marbles, and the total number of marbles is 24, the number of blue marbles is b = 24 – 16 = 8.
Correct Answer: 8

Ans: C

Explanation: The probability of winning is the number of winning tickets divided by the total number of tickets. The total number of tickets is 8 (winning) + 16 (losing) = 24 tickets.
Correct Answer: 1/3

Ans: C

Solution:
Let A be the event of rolling an odd number, so A = {1, 3, 5}.
Let B be the event of rolling a number greater than 4, so B = {5, 6}.
We want to find P(A or B), which is P(A ∪ B).
A ∪ B = {1, 3, 5, 6}.
P(A ∪ B) = (number of favorable outcomes) / (total number of outcomes) = 4/6 = 2/3.

Answer: 2/3

Ans: D

Explanation: The probability that two students don’t share a birthday is the complement of the probability that two students do share a birthday. Therefore, to find the probability that two students share a birthday, subtract the probability that they don’t share a birthday from 1.

Correct Answer: 0.008

Ans: A

Solution:
The possible outcomes of two dice rolls sum to 2 are (1,1). The possible outcomes of two dice rolls sum to 12 are (6,6). There is 1 outcome that results in a sum of 2 and 1 outcome that results in a sum of 12. Thus there are 2 winning outcomes. There are 6*6 = 36 total possible outcomes. The probability of winning is 2/36 = 1/18. The probability of losing is 1 – 1/18 = 17/18.
Answer: 17/18

Ans: B

Solution:
The prime numbers on a die are 2, 3, and 5. The probability of rolling a prime is 3/6 = 1/2.
The even numbers are 2, 4, and 6. The probability of rolling an even number is 3/6 = 1/2.
Since the rolls are independent, we multiply the probabilities: (1/2) * (1/2) = 1/4.

Answer: 1/4

Ans: B

Explanation: If 3 out of 5 students are on the honor roll, then 5 – 3 = 2 out of 5 students are not on the honor roll. To find the percentage, we calculate (2/5) * 100% = 40%. The decimal equivalent of 40% is 0.4.

Correct Option: B

Ans: B

Solution:
There are 12 months in a year. The probability the second friend shares the same birth month as the first friend is 1/12.
Answer: 1/12

Ans: B

Explanation: Each coin toss has two possible outcomes: heads (H) or tails (T). Since there are 10 coin tosses, and each toss is independent, the total number of outcomes is 2 multiplied by itself 10 times, or 2^10. 2^10 = 1024.
Correct Option: B

Ans: A

Solution:
Total number of slips = 30 + 60 = 90
Number of slips marked 2 = 22 + 54 = 76
Number of slips not marked 2 = 90 – 76 = 14
Probability = 14/90 = 7/45
Answer: 7/45

Ans: A

Solution:
1. Count the scores between 40 and 70 (inclusive): 40, 42, 42, 42, 44, 45, 45, 46, 46, 46, 47, 48, 49, 50, 53, 53, 54, 54, 56, 57, 58, 59, 59, 60, 61, 61, 62, 63, 64, 64, 66. There are 31 scores.
2. Calculate the probability: 31/54.

Answer: 31/54

Ans: A

Solution:
(i) Probability = (Number of red marbles) / (Total number of marbles) = 4 / 10 = 2/5
(ii) After removing a red marble, there are 3 red and 6 blue marbles left. Total marbles = 9. Probability = (Number of blue marbles) / (Total number of marbles) = 6 / 9 = 2/3

Answer: (i) 2/5 (ii) 2/3

Ans: A

Explanation:Let $x$ be the number of times no tails occurred (both heads).
The outcome of two tails occurred three times as often as no tails, so the number of times two tails occurred is $3x$.
The result of one tail happened twice as often as no tails, so the number of times one tail occurred is $2x$.
The total number of flips is 360, so $x + 3x + 2x = 360$.
This simplifies to $6x = 360$, so $x = 60$.
The number of times two tails occurred is $3x = 3(60) = 180$.
The probability of getting two tails is the number of times two tails occurred divided by the total number of flips, which is $\frac{180}{360} = \frac{1}{2}$.

Correct Option: A