CBSE Class 8 Mathematics Statistics and Probability MCQs Set 43

Answer: (a) 3/5

Explanation:
1. The values with x² < 2 are −1, 0 and 1 (since (−2)² = 4 and 2² = 4 are too big). So 3 of the 5 equally likely numbers are favourable and the probability is 3/5.

Teacher's Note:
1. List the numbers whose square is less than 2.
2. Probability = favourable/total.

Answer: (d) 1/2

Explanation:
1. The prime numbers on a die are 2, 3 and 5, so 3 outcomes out of 6 are favourable. Probability = 3/6 = 1/2. (1 is not prime.)

Teacher's Note:
1. A prime has exactly two factors.
2. Count 2, 3 and 5 only.

Answer: (c) 1/3

Explanation:
1. Two outcomes (2 and 4) out of six are favourable, so the probability is 2/6 = 1/3.

Teacher's Note:
1. Count the favourable outcomes.
2. Simplify the fraction.

Answer: (b) 1/2

Explanation:
1. The first die shows 2, 4 or 6 in 3 of its 6 faces, whatever the second die shows (18 favourable pairs out of 36). The probability is 1/2.

Teacher's Note:
1. Only the first die matters.
2. 3 of the 6 faces are even.

Answer: (b) 12/13

Explanation:
1. There are 4 aces, so 48 cards are not aces. Probability = 48/52 = 12/13 (which is also 1 − 1/13).

Teacher's Note:
1. P(not E) = 1 − P(E).
2. P(ace) = 4/52 = 1/13.

Answer: (d) 18

Explanation:
1. When every observation is multiplied by a number a, the mean is also multiplied by a. The new mean is 3 × 6 = 18. (Check with 2, 4, 6, 8, 10: new sum 90, mean 18.)

Teacher's Note:
1. Multiplying every value multiplies the mean.
2. Test with a small set.

Answer: (c) 0

Explanation:
1. The mean is (3 + 4 + 6 + 8 + 14)/5 = 35/5 = 7. The deviations are −4, −3, −1, 1 and 7, which add up to 0. The sum of the deviations from the mean is always zero.

Teacher's Note:
1. Find the mean first.
2. Positive and negative deviations cancel exactly.

Answer: (c) 10/21

Explanation:
1. The number of ways to draw 2 balls from 7 is 7C2 = 21. The ways to draw 2 non-blue balls from the 5 red and green balls is 5C2 = 10. So the probability is 10/21.

Teacher's Note:
1. Count pairs, not single balls.
2. Non-blue balls: 2 + 3 = 5.

Answer: (d) 2/13

Explanation:
1. There are 4 jacks and 4 kings, so 8 favourable cards. Probability = 8/52 = 2/13.

Teacher's Note:
1. Add the favourable cards of both kinds.
2. Simplify 8/52.

Answer: (c) 1/6

Explanation:
1. Only the number 6 on the die is a multiple of 6, so the probability is 1/6.

Teacher's Note:
1. Multiples of 6 on a die: only 6.
2. One favourable outcome out of 6.

Answer: (b) 0

Explanation:
1. The face cards are the kings, queens and jacks. All of them have been removed, so no face card is left.

Teacher's Note:
1. Face cards are K, Q and J.
2. They have all been taken out.

Answer: (a) 0

Explanation:
1. None of the six angles measures 90°, so the number of favourable outcomes is 0 and the probability is 0 (an impossible event).

Teacher's Note:
1. Look for an angle of exactly 90°.
2. No favourable outcome means probability 0.

Answer: (d) 0

Explanation:
1. The exterior angles are 140°, 120° and 100°, all obtuse. No exterior angle is acute, so the probability is 0.

Teacher's Note:
1. An acute angle is less than 90°.
2. Check the exterior angles only.

Answer: (c) 1

Explanation:
1. All six angles (40°, 60°, 80°, 140°, 120°, 100°) are less than 180°. So the event is certain and its probability is 1.

Teacher's Note:
1. Compare each angle with 180°.
2. A certain event has probability 1.

Answer: (a) 1/12

Explanation:
1. The favourable outcomes are (1, 1), (3, 3) and (5, 5): 3 out of 36, so the probability is 3/36 = 1/12.

Teacher's Note:
1. A doublet means both dice show the same number.
2. Only odd numbers count.

Answer: (d) 1/12

Explanation:
1. A sum greater than 10 means 11 or 12: (5, 6), (6, 5) and (6, 6). That is 3 outcomes out of 36, so the probability is 1/12.

Teacher's Note:
1. List the outcomes with sum 11 and 12.
2. Count them.

Answer: (c) 1/3

Explanation:
1. The numbers strictly between 3 and 6 are 4 and 5, so 2 outcomes out of 6 are favourable. Probability = 1/3.

Teacher's Note:
1. 'Between' excludes 3 and 6.
2. Count the remaining numbers.

Answer: (c) 1/4

Explanation:
1. The four outcomes HH, HT, TH, TT are equally likely and only TT has no head, so the probability is 1/4.

Teacher's Note:
1. List all four outcomes.
2. No head means both tails.

Answer: (b) 1/2

Explanation:
1. At least two heads means exactly two (HHT, HTH, THH) or three (HHH), which is 4 outcomes out of 8. Probability = 4/8 = 1/2.

Teacher's Note:
1. Add the cases of two and three heads.
2. Total outcomes = 8.

Answer: (d) 1/26

Explanation:
1. There are two black suits (spades and clubs), each with one ten, so 2 favourable cards. Probability = 2/52 = 1/26.

Teacher's Note:
1. Black suits: spades and clubs.
2. One ten in each suit.

Answer: (c) 1/12

Explanation:
1. The doublets of even numbers are (2, 2), (4, 4) and (6, 6): 3 outcomes out of 36. Probability = 3/36 = 1/12.

Teacher's Note:
1. A doublet has the same number on both dice.
2. Even numbers: 2, 4, 6.

Answer: (b) 8

Explanation:
1. Number of green marbles = 2/3 × 24 = 16. So the number of blue marbles is 24 − 16 = 8.

Teacher's Note:
1. Find the green marbles first.
2. Blue = total − green.

Answer: (a) 32

Explanation:
1. Arrange in order: 21, 24, 27, 30, 32, 34, 35, 38, 48. There are 9 values, so the median is the 5th value, 32.

Teacher's Note:
1. Always arrange the data first.
2. For an odd count the median is the middle term.

Answer: (d) 120

Explanation:
1. The frequencies are 120 → 4, 110 → 2, 130 → 2 and 140 → 2. The highest frequency belongs to 120, so the mode is 120.

Teacher's Note:
1. Mode is the most frequent value.
2. Tally the frequencies.

Answer: (c) 1/3

Explanation:
1. The favourable outcomes are 5 and 6, so the probability is 2/6 = 1/3.

Teacher's Note:
1. 'Greater than 4' excludes 4.
2. Count 5 and 6.