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Chapter 9: Problem 22

Find the probability for the experiment of drawing a card at random from a standard deck of 52 playing cards. The card is not a face card.

Short Answer

Expert verified
The probability of drawing a non-face card from a standard deck is \(10/13\).

Step by step solution

01

Total outcomes

Start by figuring out the total outcomes. In this case, the total outcomes are 52 because there are 52 cards in a deck.
02

Favorable outcomes

Find out the favorable outcomes for this exercise. The problem states the card drawn should not be a face card. In a standard deck there are 12 face cards. Subtraction of the number of face cards from the total cards gives the number of non-face cards. So, \(52-12 = 40\). There are 40 favorable outcomes in this case.
03

Probability formula

Substitute the total and favorable outcomes in the probability formula. Probability (P) = Favorable outcomes / Total outcomes. Therefore, \(P = 40/52 \).
04

Simplify the fraction

Simplify the result by factoring out the Greatest Common Divisor (GCD). Both 40 and 52 can be divided by 4, so the simplified fraction is \(10/13\).

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