CBSE Class 9 Maths Ganita Manjari Part 1 Ch 07 The Mathematics of Maybe Introduction to Probability MCQs with Answers Set 01

Answer: (a) \( \frac{9}{10} \)

Explanation:
1. Books that are not magazines = 100 − 10 = 90.
2. P(not a magazine) = \( \frac{90}{100} = \frac{9}{10} \).

Answer: (a) Yes, probability = \( \frac{5}{8} \)

Explanation:
1. Total marbles = 5 + 3 = 8.
2. P(red) = \( \frac{5}{8} = 0.625 \), which is more than \( \frac{1}{2} \). The student is right.

Answer: (a) P(number greater than 4) = \( \frac{1}{3} \)

Explanation:
1. Numbers greater than 4 on a die: 5 and 6, which is 2 outcomes out of 6.
2. P = \( \frac{2}{6} = \frac{1}{3} \).

Answer: (c) \( \frac{4}{5} \)

Explanation:
1. Good bulbs = 20 − 4 = 16.
2. P(not defective) = \( \frac{16}{20} = \frac{4}{5} \).

Answer: (b) \( \frac{1}{4} \)

Explanation:
1. There are 4 equally likely outcomes and only one of them is C.
2. P(C) = \( \frac{1}{4} \).

Answer: (b) No, probability = \( \frac{1}{13} \)

Explanation:
1. A deck has 4 kings (one in each suit).
2. P(king) = \( \frac{4}{52} = \frac{1}{13} \), not \( \frac{1}{26} \).

Answer: (a) \( \frac{4}{10} \)

Explanation:
1. Primes from 1 to 10: 2, 3, 5, 7, which is 4 numbers. (1 is not prime.)
2. P(prime) = \( \frac{4}{10} = \frac{2}{5} \).

Answer: (a) \( \frac{1}{4} \)

Explanation:
1. Multiples of 4 up to 40: 4, 8, …, 40, which is 40 ÷ 4 = 10 numbers.
2. P = \( \frac{10}{40} = \frac{1}{4} \).

Answer: (a) Probability of black = \( \frac{2}{5} \)

Explanation:
1. Total balls = 6 + 4 = 10.
2. P(black) = \( \frac{4}{10} = \frac{2}{5} \). (\( \frac{3}{5} \) is the probability of white.)

Answer: (a) Probability of black < probability of white

Explanation:
1. P(black) = \( \frac{4}{10} \) and P(white) = \( \frac{6}{10} \).
2. Since 4 < 6, black is less likely than white.

Answer: (c) Probability of composite < probability of prime

Explanation:
1. Primes on a die: 2, 3, 5, so P(prime) = \( \frac{3}{6} \).
2. Composites on a die: 4, 6, so P(composite) = \( \frac{2}{6} \). (1 is neither prime nor composite.)
3. \( \frac{2}{6} < \frac{3}{6} \).

Answer: (a) \( \frac{1}{5} \)

Explanation:
1. Only Maths = 18 − 10 = 8 students.
2. P(only Maths) = \( \frac{8}{40} = \frac{1}{5} \).

Answer: (d) \( \frac{4}{5} \)

Explanation:
1. Medals that are not for basketball = 100 − 20 = 80.
2. P = \( \frac{80}{100} = \frac{4}{5} \).

Answer: (a) \( \frac{17}{24} \)

Explanation:
1. Novels or science = 100 + 70 = 170.
2. P = \( \frac{170}{240} = \frac{17}{24} \).

Answer: (a) \( \frac{11}{12} \)

Explanation:
1. Votes for a candidate = 70 + 40 = 110.
2. P = \( \frac{110}{120} = \frac{11}{12} \).

Answer: (b) No, because probability of tail = \( \frac{1}{2} \)

Explanation:
1. A fair coin has two equally likely outcomes.
2. P(head) = P(tail) = \( \frac{1}{2} \), so head is not more likely than tail.

Answer: (b) \( \frac{1}{2} \)

Explanation:
1. Outcomes: HH, HT, TH, TT, which is 4 equally likely outcomes.
2. Exactly one head: HT and TH, which is 2 outcomes.
3. P = \( \frac{2}{4} = \frac{1}{2} \).

Answer: (a) \( \frac{7}{50} \)

Explanation:
1. Perfect squares from 1 to 50: 1, 4, 9, 16, 25, 36, 49, which is 7 numbers.
2. P = \( \frac{7}{50} \).

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. P(red) = \( \frac{5}{8} \) and P(blue) = \( \frac{3}{8} \), so red is more likely. The Assertion is true.
2. With the same total (8), more favourable outcomes means a larger probability. The Reason is true.
3. Red has more favourable outcomes (5 > 3), so R correctly explains A.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. P(invalid) = \( \frac{10}{120} = \frac{1}{12} \).
2. P(valid) = \( 1 - \frac{1}{12} = \frac{11}{12} \). The Assertion is true.
3. The Reason is the complement rule, which is true and gives the Assertion directly.