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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

Why is probability theory important to statistics?

Suppose that A, B, C are three events that cannot all occur simultaneously. Does this condition necessarily imply that A, B, and C are mutually exclusive ? Justify your answer and illustrate it with a venn diagram.

What is the difference between selecting a member at random from a finite population and taking a simple random sample of size 1?

In each of Exercises 5.167-5.172, we have provided the number of trials and success probability for Bernoulli trials. Let X denote the total number of successes. Determine the required probabilities by using

(a) the binomial probability formula, Formula 5.4 on page 236. Round your probability answers to three decimal places.

(b) Table VII in Appendix A. Compare your answer here to that in part (a).

n=4,p=0.3,P(X=2)

Answer true or false to the following statement and justify your answer. If event A and event B are mutually exclusive, neither are events A,B and C for every event C.
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