What can be said about the cardinalities of the sample spaces of the events below? Event A: Drawing a card from a standard deck of playing cards Event B: Rolling a standard number cube A. The cardinality of event A's sample space is 46 greater than event B's. B. The cardinality of event B's sample space is 46 greater than event A's. C. The cardinality of event B's sample space is 6 greater than event A's. D. The cardinality of event A's sample space is 6 greater than event B's.

Question

Mathematics

Hanna Hensley

19 October, 01:32

What can be said about the cardinalities of the sample spaces of the events below? Event A: Drawing a card from a standard deck of playing cards Event B: Rolling a standard number cube A. The cardinality of event A's sample space is 46 greater than event B's. B. The cardinality of event B's sample space is 46 greater than event A's. C. The cardinality of event B's sample space is 6 greater than event A's. D. The cardinality of event A's sample space is 6 greater than event B's.

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Mckinley Hammond · Answer 1

Sample space of the given events contain all the possible outcomes of the event. Cardinality of a set is defined as the number of elements in that set.

For Event A:

The sample space comprises all the 52 outcomes of cards in the deck.

So cardinality of event A = n (A) = 52

For Event B:

The sample space comprises all the 6 outcomes of rolling a dice.

So cardinalty of event B = n (B) = 6

The difference in two is 52 - 6 = 46

So, we can conclude that the cardinality of sample space of event A is 46 more than the event B's sample space.

Thus the correct answer is option A