What is the probability of this event? Original Problem in Description below.

Question

An ordinary deck of cards contains 52 cards divided into four suits. The red suits are diamonds (◆) and hearts (♥), and the black suits are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards.

Imagine choosing a card at random from a thoroughly mixed deck. Consider the event that the chosen card is black and has an even number on it.

What is the probability of this event?

Answer 1

Probability of Black and Even Number

Spades

2

4

6

8

10

Clubs

2

4

6

8

10

There are 10 outcomes in the sample space that are both black and even, thus

P(Black and Even Number) = 10/52 = 5/26 = approximately 0.192 as a decimal or 19.2% as a percent