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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)14

Part (b)12

Part (c)34

Step by step solution

01

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.

02

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:

PE=No.offavorableoutcomeTotalno.ofoutcomes=1352=14

03

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:

=2652=12

04

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:

=3952=34

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Most popular questions from this chapter

World Series. The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919鈥�1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than seven games to establish a winner. From the document World Series History on the Baseball Almanac website, as of November 2013, the lengths of the World Series are as given in the following table

Number of GamesFrequencyRelative Frequency
4210.200
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6240.229
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a. If X denotes the number of games that it takes to complete a World Series, identify the possible values of the random variable X.

b. Do the first and third columns of the table provide a probability distribution for X? Explain your answer.

c. Historically, what is the most likely number of games it takes to complete a series?

d. Historically, for a randomly chosen series, what is the probability that it ends in five games?

e. Historically, for a randomly chosen series, what is the probability that it ends in five or more games?

f. The data in the table exhibit a statistical oddity. If the two teams in a series are evenly matched and one team is ahead three games to two, either team has the same chance of winning game number six. Thus there should be about an equal number of six-and seven-game series. If the teams are not evenly matched, the series should tend to be shorter, ending in six or fewer games, not seven games. Can you explain why the series tend to last longer than expected?

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A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing straws. The person getting the longest straw will be appointed chairperson, and the one getting the shortest straw will be appointed secretary. The possible outcomes can be represented in the following manner.

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