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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

Suppose that A and B are events such that P(A)=14,P(B)=13and P(AorB)=12

Part (a). Are event A and B mutually exclusive ? Explain your answer.

Part (b) FindP(A&B)

Suppose that C and D are mutually exclusive events such that P(C)=0.14andP(D)=0.32 Determine P(CorD).

Expected Utility. One method for deciding among various investment involves the concept of expected utility. Economists describe the importance of various levels of wealth by using utility functions. For instance, in most case, a single dollar is more important (has greater utility ) for someone with little wealth than for someone with greater wealth Consider two investments, say investment A and B. Measured in thousand of dollars, suppose that investment A yields 0, 1, and 4 with probability 0.1 and16 with probability 0.5, 0.3 and 0.2 respectively. Let Y denote the yield of an investment. For the two investment, determine and compare.

Part (a) The mean of Y, the expected yield.

Part (b) The mean of Y,the expected utility, using the utility function role="math" localid="1651845051902" 蠀y=yInterpret the utility function u

Part (c) The mean of y3/2,the expected utility, using the utility function v(y)=y3/2. Interpret the utility function v

ASU Enrollment Summary. According to the Arizona State University Enrollment Summary, a frequency distribution for the number of undergraduate students attending Arizona State University ( ASU ) in the Fall 2012 semester, by class level, is as shown in the following table. Here , 1 = freshman , 2 = sophomore , 3 = junior , and 4 = senior.

Class level
1234
No. of students
9,652
11,115
17,302
21,114

Let X denote the class level of a randomly selected ASU undergraduate.

(a) What are the possible values of the random variable X?

(b) Use random-variable notation to represent the event that the student selected is a junior ( class - level 3 ).

(c) Determine P ( X = 3 ), and interpret your answer in terms of percentages.

(d) Determine the probability distribution of the random variable X.

(e) Construct a probability histogram for the random variable X.

A variable y of a finite population has the following frequency distribution:

y1234
f22106

Suppose a member is selected at random from the population and let Y denote the value of the variable y for the member obtained.

a. Determine the probability distribution of the random variable Y.

b. Use random-variable notation to describe the events that Y takes on the value 3, a value less than 3, and a value of at least 3.

c. Find P(Y = 3), P(Y <3), and P(Y 鈮� 3). Interpret your results.

d. Construct a probability histogram for the random variable Y.
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