Question

A special deck of cards has ten cards. Four are green (G), four are blue (B), and two are red (R). When a card is picked, the color of it is recorded. An experiment consists of first picking a card and then tossing a coin, which lands on heads (H) or tails (T).
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?
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 C mutually exclusive?

Answer 1

Answer:

{GT, GH, BT, BH, RT, RH};

1 /5;

Mutually exclusive ;

Not mutually exclusive.

Step-by-step explanation:

Given :

Green cards, G = 4

Blue cards, B = 4

Red cards, R = 2

For a coin toss :

{H, T}

A card is picked, then a coin is tossed :

Sample space :

{GT, GH, BT, BH, RT, RH}

2.) probability of picking a green card, then probability of landing a head on a coin toss

P(A) = number of required outcome / Total possible outcomes

P(A) = P(green card) * P(Head)

P(A) = (4 / 10) * (1/2)

P(A) = 4 /20

P(A) = 1/5

C.)

Both A and B are mutually exclusive, since both event A and event B cannot occur together, since both red and green cannot be picked during a single pick, this either a red is picked or green is picked, then they are A and B are mutually exclusive.

D.) Event A and C are not mutually exclusive, picking a green card, event A and picking a red or blue card, event B. Both event can happen simultaneously, hence, event A and B are not mutually exclusive.