Chapter 5: Q 5.14. (page 200)

Playing Cards. An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs- with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is
(a). a spade? (b). red? (c). not a club?

Short Answer

Expert verified

Part (a) $\frac{1}{4}$

Part (b) $\frac{1}{2}$

Part (c) $\frac{3}{4}$

Step by step solution

Part (a) Step 1. Given information.

The given statement is:

An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs- with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red.

Part (a) Step 2. Find the probability that the selected card is a spade.

There are 52 cards in total and 13 cards are spade in it.

probability of getting a spade is:

$P (E) = \frac{No . of favorable outcome}{Total no . of outcomes} = \frac{13}{52} = \frac{1}{4}$

Part (b) Step 2. Find the probability that the selected card is red.

The number of red cards in a deck of 52 is 13 for the heart and 13 for the diamond.

Therefore, the total of red cards is 26.

The probability of getting a red card is:

$= \frac{26}{52} = \frac{1}{2}$

Part (b) Step 2. Find the probability that the selected card is not a club.

There are 13 clubs in a deck of 52 cards.

There are 39 cards that aren't club cards.

The probability of not getting a club is:

$= \frac{39}{52} = \frac{3}{4}$

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Short Answer

Step by step solution

Part (a) Step 1. Given information.

Part (a) Step 2. Find the probability that the selected card is a spade.

Part (b) Step 2. Find the probability that the selected card is red.

Part (b) Step 2. Find the probability that the selected card is not a club.

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