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, 3 or 4 is rolled first, followed by landing a head on the coin toss. P(A) = Present your answer as a decimal rounded to two decimal places. C. Let B be the event that a number less than 2 is rolled, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? (Yes or No)

Answer 1

Answer:

A) There are 12 elements in the sample space.

B) The required probability is 1/4 or 0.25.

C) Yes, the events are mutually exclusive.

Step-by-step explanation:

Consider the provided information.

Part(A)

An experiment consists of first rolling a die and then tossing a coin.

Thus the sample space is:

(1,H), (2,H) (3,H) (4,H) (5,H), (6,H)

(1,T), (2,T) (3,T) (4,T) (5,T), (6,T)

Hence, there are 12 elements in the sample space.

Part(B) Let A be the event that either a 2, 3 or 4 is rolled first, followed by landing a head on the coin toss.

Now consider the above sample space. There are 3 possible case in which 2, 3 or 4 is rolled first, followed by landing a head on the coin toss.

i.e (2,H) (3,H) (4,H)

The required probability is: P(A)=$\frac{3}{12}=\frac{1}{4}=0.25$

Hence, the required probability is 1/4 or 0.25.

Part(C)

Mutually exclusive, means that they cannot occur at the same time.

From part (B) Event A = (2,H) (3,H) (4,H)

Let B be the event that a number less than 2 is rolled, followed by landing a head on the coin toss.

Thus, the Event B = (1,H).

Therefore, Event A and B can't be occur at the same time as P(A and B)=0.

Hence, yes, the events are mutually exclusive.