Q. 87 A special deck of cards has ten ... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 3: Q. 87 (page 224)

A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
a. List the sample space.
b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find $P (A)$ .
c. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.
d. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and Cmutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.

Short Answer

Expert verified

(a)

$S = \{\begin{array}{l} (Green, H), (Blue, H), (Red, H) \\ (Green, T), (Blue, T), (Red, T) \end{array}\}$

(b) $P (A) = 0.15$

(d)The eventsA andB are not mutually exclusive.

Step by step solution

Given information (part a)

A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.

Explanation (part a)

The experiment consists of first picking a card and then tossing a coin. Sample space consists of all the possible outcomes.

$S = \{\begin{array}{l} (Green, H), (Blue, H), (Red, H) \\ (Green, T), (Blue, T), (Red, T) \end{array}\}$

Given information (part b)

Explanation (part b)

The total number of possible outcomes $= 6$

Let A be that a blue card is picked first, followed by a head-on the coin toss is calculated as

$P (A) = \frac{3}{10} 脳 \frac{1}{2} P (A) = \frac{3}{20} P (A) = 0.15$

Given information (part c)

Explanation (part c)

Let A be that a blue card is picked first, followed by a head-on coin toss.

LetB be the event that a red or green is picked, followed by a head on the coin toss. We observe that is not a common outcome in events A and B. Thus, events A and B are mutually exclusive.

Given information (part d)

Explanation (part d)

Let A be that a blue card is picked first, followed by a head-on coin toss.

Let C be the event that a red or blue is picked, followed by a head on the coin toss. We observe that there are few common outcomes in events A andC. Thus, events A and C are not mutually exclusive.