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 $P\left(A\right)$.

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.

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.

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

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

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.

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

$$\begin{gathered} P\left(A\right)=\frac{3}{10}\times \frac{1}{2} \\ P\left(A\right)=\frac{3}{20} \\ P\left(A\right)=0.15 \end{gathered}$$

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.

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.

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.

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.