Question

A special deck of cards has 12 cards. four are green, three are blue, and five are red. When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin. A. How many elements are there in the sample space? 12 B. Let A be the event that a green card is picked first, followed by landing a tail on the coin toss. P(A) = Present your answer as a decimal number rounded to two decimal places of accuracy. C. Let C be the event that a green or red is picked, followed by landing a tail on the coin toss. Are the events A and C mutually exclusive?(Yes or No) D. Let B be the event that a blue or red is picked, followed by landing a tail on the coin toss. Are the events A and B mutually exclusive? (Yes or No)

Answer 1

Answer:

A. Sample space = 6

B. 0.17

C. No

D. Yes

Step-by-step explanation:

A. The sample space of an experiment is the set of all possible outcomes of that experiment.

since there are three colours and 2 outcomes for a coin toss,

sample space = 3 * 2 = 6

B. Probability of picking a green first = 4/12 = 1/3

probability of a tail = 1/2

Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17

C. No.

Considering the two events;

A; green card is picked first

C ; a green or red card is picked

There is an intersection point for the two events.  Therefore, they are not mutually exclusive.

D. Yes.

Considering the two events;

A; green card is picked first

B ; a blue or red card is picked

There is no intersection point for the two events. Therefore, they are mutually exclusive.