Question

an experiment consists of first rolling a die and then tossing a coin:
a. how many elements are there in the sample space?
b. let a be the event that either a 2 or 3 is rolled first, followed by landing a head on the coin toss. p(a) = present your answer as a decimal rounded to four decimal places.
c. let b be the event that a number less than 3 is rolled, followed by landing a head on the coin toss. are the events a and b mutually exclusive?
no, they are not mutually exclusive
yes, they are mutually exclusive

Explanation:

a. Step1: Die (6) and coin (2) outcomes.

Sample space size = 6×2=12

b. Step1: A has 2 die (2,3) ×1 coin (H) = 2 outcomes.

Step2: P(A)=2/12≈0.1667

c. Step1: A: (2,H),(3,H); B: (1,H),(2,H).

Step2: Shared (2,H), not mutually exclusive.

Answer:

a. 12
b. 0.1667
c. No, they are not Mutually Exclusive