Statistics and Probability — Practice

Question 1

The mean of 2, 4, 6, 8, 10 is:
(a) 5 (b) 6 (c) 7 (d) 8

Accepted Answer

(b) 6.

Sum = 30, count = 5, mean = 6.

Question 2

The median of 3, 7, 5, 1, 9 is:
(a) 3 (b) 5 (c) 7 (d) 9

Accepted Answer

(b) 5.

Sorted: 1, 3, 5, 7, 9 → the middle term is 5.

Question 3

The mode of 2, 3, 3, 4, 5, 3, 6 is:
(a) 2 (b) 3 (c) 4 (d) 6

Accepted Answer

(b) 3.

3 occurs three times — more than any other value.

Question 4

A fair die is rolled once. The probability of getting an even number is:
(a) 1/3 (b) 1/2 (c) 2/3 (d) 1/6

Accepted Answer

(b) 1/2.

Favourable: 2, 4, 6 → 3 of 6 → 1/2.

Question 5

Two fair coins are tossed together. The probability of getting exactly one head is:
(a) 1/4 (b) 1/2 (c) 3/4 (d) 1/3

Accepted Answer

(b) 1/2.

Outcomes {HH, HT, TH, TT}; exactly one head in HT, TH → 2/4 = 1/2.

Question 6

For a distribution the mean is 30 and the median is 28. The mode is:
(a) 22 (b) 24 (c) 26 (d) 32

Accepted Answer

(b) 24.

Mode = 3 × Median − 2 × Mean = 84 − 60 = 24.

Question 7

Two dice are thrown together. The probability that the sum of the numbers is 7 is:
(a) 1/6 (b) 1/9 (c) 1/12 (d) 5/36

Accepted Answer

(a) 1/6.

Sum 7 arises in 6 of 36 outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6/36 = 1/6.

Question 8

One card is drawn at random from a well-shuffled pack of 52. The probability that it is a king is:
(a) 1/13 (b) 1/26 (c) 4/13 (d) 1/4

Accepted Answer

(a) 1/13.

4 kings out of 52 → 4/52 = 1/13.

Question 9

A bag contains 4 red and 6 blue balls. Two balls are drawn one after another without replacement. The probability that both are red is:
(a) 2/15 (b) 4/25 (c) 1/6 (d) 3/20

Accepted Answer

(a) 2/15.

(4/10) × (3/9) = 12/90 = 2/15 — the total drops from 10 to 9 after the first draw.

Question 10

A card is drawn from a pack of 52. The probability that it is a red card or a king is:
(a) 7/13 (b) 15/26 (c) 1/2 (d) 4/13

Accepted Answer

(a) 7/13.

P(red or king) = 26/52 + 4/52 − 2/52 = 28/52 = 7/13. The 2 red kings are subtracted once to avoid double counting.

Practice — Statistics and Probability

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