Problem 742

An experiment consists of drawing 1 card from a standard 52-card deck. What is the probability of drawing an 8?




A standard deck of 52 cards has four 13-card suits: diamonds, hearts, clubs and spades. The diamonds and hearts are red, and the clubs and spades are black. Ecah 13-card suit contains cards numbered from 2 to 10, a jack, a queen, a king and an ace. The jack, queen, and king are called face cards.

Drawing 1 card implies that each simple event in sample space S is as likely to occur as any other. Therefore, the probability of an arbitrary event E in S is given by the formula below.


The sample space S is the set of the 52 cards in a standard deck.

n(S) = 52

Let Q = the card is an 8. There are 4 element Q in the sample space.

n(Q) = 4

Substitute the value for n(Q)  and n(S).

P(Q) = \frac{n(Q)}{n(S)}


Therefore , the probability of drawing an 8 is \frac{1}{13}.


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