Probability — Practice

Question 1

A die is rolled. What is the probability of getting an even number?

Accepted Answer

Step 1 — Even numbers: 2, 4, 6 (3 favourable), total 6.

Step 2 — P = 3/6 = 1/2.

✦ Answer: 1/2.

Question 2

One card is drawn from a well-shuffled deck. Find P(getting a king).

Accepted Answer

Step 1 — 4 kings out of 52 cards.

Step 2 — P = 4/52 = 1/13.

✦ Answer: 1/13.

Question 3

If P(E) = 0.35, find P(not E).

Accepted Answer

Step 1 — P(not E) = 1 − 0.35 = 0.65.

✦ Answer: 0.65.

Question 4

A bag has 5 red, 8 white and 7 blue marbles. One is drawn at random. Find P(not white).

Accepted Answer

Step 1 — Total = 20; white = 8, so not-white = 12.

Step 2 — P(not white) = 12/20 = 3/5.

✦ Answer: 3/5.

Question 5

Two dice are thrown. Find the probability that the sum is 7.

Accepted Answer

Step 1 — Total outcomes = 36. Favourable: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6.

Step 2 — P = 6/36 = 1/6.

✦ Answer: 1/6.

Question 6

A card is drawn from a deck. Find P(a red face card).

Accepted Answer

Step 1 — Red face cards = J, Q, K of hearts and diamonds = 6.

Step 2 — P = 6/52 = 3/26.

✦ Answer: 3/26.

Question 7

Two coins are tossed together. Find the probability of getting at least one head.

Accepted Answer

Step 1 — Sample space {HH, HT, TH, TT}; P(no head) = P(TT) = 1/4.

Step 2 — P(at least one head) = 1 − 1/4 = 3/4.

✦ Answer: 3/4.

Question 8

A bag has 12 balls, some white. If the probability of drawing a white ball is 3 times that of a non-white ball, find the number of white balls.

Accepted Answer

Step 1 — Let white = w, so non-white = 12 − w.

Step 2 — w/12 = 3 × (12−w)/12 ⇒ w = 3(12 − w) = 36 − 3w.

Step 3 — 4w = 36 ⇒ w = 9.

✦ Answer: 9 white balls.

Question 9

Two dice are thrown. Find the probability that the product of the numbers is 12.

Accepted Answer

Step 1 — Total = 36. Products = 12: (2,6),(6,2),(3,4),(4,3) = 4 outcomes.

Step 2 — P = 4/36 = 1/9.

✦ Answer: 1/9.

Question 10

All kings and queens are removed from a deck. A card is drawn from the remaining 44. Find P(getting a red card).

Accepted Answer

Step 1 — Removed 4 kings + 4 queens = 8, leaving 44. Red removed = 2 kings + 2 queens = 4, so red left = 26 − 4 = 22.

Step 2 — P = 22/44 = 1/2.

✦ Answer: 1/2.

Practice — Probability

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