﻿ Probability Worksheets - Page 4 | Problems & Solutions

# Probability Worksheets - Page 4

Probability Worksheets
• Page 4
31.
Fifteen cards labeled A through O are placed in a bag. The bag is shaken and one card is drawn at random. Find the odds in favor of drawing a vowel.
 a. 11 : 4 b. 1 : 2 c. 4 : 11 d. 5 : 11

#### Solution:

Odds in favor of getting a vowel are 4 : 11
[ Four of the outcomes are successes and 11 outcomes are failures.]

32.
A coin is tossed. Write the sample space.
 a. {T} b. {H, T} c. { } d. {H}

#### Solution:

Each outcome is a head (H) or a Tail (T)

Sample space, S = {H, T}.

33.
When a die is rolled, specify the event of getting an odd number.
 a. {4, 5, 6} b. {1, 3, 5} c. {1, 2, 3, 4, 5, 6} d. {1, 2, 3}

#### Solution:

There are three odd numbers: 1, 3, 5, when a die is rolled.

34.
A die is rolled. Find the probability of an event getting an even number.
 a. $\frac{1}{4}$ b. $\frac{1}{3}$ c. $\frac{1}{2}$ d. $\frac{1}{6}$

#### Solution:

P(getting an even number) = 3 / 6 = 1 / 2
[There are three even numbers 2, 4, 6.]

35.
A die is rolled. Find the probability of getting 3 or 6.
 a. $\frac{1}{3}$ b. $\frac{1}{2}$ c. $\frac{1}{6}$ d. $\frac{1}{4}$

#### Solution:

P(getting 3 or 6) = 2 / 6 = 1 / 3
[There are 2 ways to roll one of these numbers.]

36.
A die is rolled. Find the probability of getting a number 8.
 a. $\frac{1}{6}$ b. 1 c. $\frac{1}{3}$

#### Solution:

P(getting 8) = 0 / 6 = 0
[There is no way to get an 8.]

37.
Two coins are tossed. Find the probability of getting 2 tails.
 a. 1 b. $\frac{1}{4}$ c. $\frac{1}{2}$

#### Solution:

Sample space, S = {(H, H), (H, T), (T, H), (T, T)}

P(getting exactly 2 tails) = 1 / 4
[There is only one way to get 2 tails: (T, T).]

38.
Three coins are tossed. Write the number of elements in the sample space.
 a. 4 b. 6 c. 2 d. 8

#### Solution:

Sample space, S = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}

Number of elements in sample space is 8.

39.
Find the probability of getting exactly 2 heads when 3 coins are tossed.
 a. $\frac{1}{2}$ b. $\frac{1}{4}$ c. $\frac{3}{8}$ d. $\frac{7}{8}$

#### Solution:

Sample space, S = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}

There are 3 ways to get exactly 2 heads: (H, H, T), (H, T, H), (T, H, H).

P (getting exactly 2 heads) = 3 / 8

40.
Find the probability of getting more than one head, when 3 coins are tossed.
 a. $\frac{7}{8}$ b. $\frac{3}{8}$ c. $\frac{1}{8}$ d. $\frac{1}{2}$

#### Solution:

Sample space, S = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (H, T, T), (T, H, T), (T, T, H), (T, T, T)}

There are 4 ways to get more than one head: (H, H, T), (H, T, H), (T, H, H), (H, H, H)

P (getting more than one head) = 4 / 8 = 1 / 2