Question

what can be said about the cardinalities of the sample spaces of the events below? Event A: Flipping a coin Event B: Rolling a standard number cube

A.
The cardinality of event A’s sample space is 8 greater than event B’s.
B.
The cardinality of event B’s sample space is 8 greater than event A’s.
C.
The cardinality of event B’s sample space is 4 greater than event A’s.
D.
The cardinality of event A’s sample space is 7 greater than event B’s.

Answer 1

Answer:  The correct option is

(C). The cardinality of event B’s sample space is 4 greater than event A’s.

Step-by-step explanation:  We are given to select the correct statement about the cardinalities of the sample spaces of the following events :

Event A : Flipping a coin.

Event B : Rolling a standard number cube.

We know that

there are two possible outcomes for the event of flipping a coin, i.e., Head (H) and Tail (T).

So, the sample space S for event A is given by

S = {H, T}   ⇒    n(S) = 2.

And, there are six possible outcomes for the event of rolling a standard number cube, i.e., 1, 2, 3, 4, 5 and 6.

So, the sample space S' for event B is given by

S' = {1, 2, 3, 4, 5, 6}   ⇒  n(S'} = 6.

Therefore, the difference in the cardinalities of the events A and B is

n(S') - n(S) = 6 - 2 = 4.

Thus, the cardinality of event B’s sample space is 4 greater than event A’s.

Option (C) is CORRECT.