Question

A special deck of cards has 8 green cards , 13 blue cards , and 6 red cards . When a card is picked, the color 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?
b. Let A be the event that a green card is picked first, followed by landing a head on the coin toss.
Incorrect Round your answer to 4 decimal places.
c. Let B be the event that a red or blue 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 green or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive?

Answer 1

a. The sample space has 6 elements. b. P(A) = 4/17. c. Events A and B are mutually exclusive. d. Events A and C are not mutually exclusive.

Step-by-step explanation:

a. The sample space for this experiment consists of the color of the card and the outcome of the coin toss. Since there are 3 colors and 2 possible outcomes for the coin toss, the sample space has a total of 3 * 2 = 6 elements.

b. Let's calculate the probability of event A which is picking a green card first and landing a head on the coin toss. There are 8 green cards and 2 possible outcomes for the coin toss (H or T). So, the probability of event A is P(A) = 8/17 * 1/2 = 4/17 = 0.2353 (rounded to 4 decimal places).

c. Event A is picking a green card first followed by landing a head on the coin toss. Event B is picking a red or blue card first followed by landing a head on the coin toss. The events A and B are mutually exclusive because there are no outcomes that satisfy both events, therefore P(A and B) = 0.

d. Event C is picking a green or blue card first followed by landing a head on the coin toss. The events A and C are not mutually exclusive because there is a possibility of drawing a green card and satisfying event A as well as event C. Therefore, P(A and C) > 0.