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)=
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.