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Chapter 5: Q. 72 (page 350)

A standard deck of playing cards (with jokers removed) consists of 52cards in four suits鈥攃lubs, diamonds, hearts, and spades. Each suit has 13cards, with denominations ace,2,3,4,5,6,7,8,9,10jack, queen, and king. The jacks, queens, and kings are referred to as 鈥渇ace cards.鈥� Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

Are the events 鈥渉eart鈥� and 鈥渇ace card鈥� independent? Justify your answer.

Short Answer

Expert verified

Yes, the two events are independent.

Step by step solution

01

Step 1. Given information

The table is:

02

Step 2. Concept used

The condition for the independent events is:

P(A鈭�B)=P(A)脳P(B)

03

Step 3. Calculation

Consider, X be the event that shows the heart card and Y be the event that shows the face card.

Here,

P(X)=NumberofheartcardsTotalcards=1352=14

P(Y)=NumberoffacecardsTotalcards=1252=313P(X鈭�Y)=332

Now check the required condition as:

P(X鈭�Y)=P(X)脳P(Y)352=14脳313352=352

Since, the required condition is satisfied. Thus, it could be said that the events 鈥渇ace card鈥� and 鈥渉eart鈥� are independent.

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Most popular questions from this chapter

Bull鈥檚-eye! In a certain archery competition, each player continues to shoot until he or she misses the center of the target twice. Quinn is one of the archers in this competition. Based on past experience, she has a 0.60probability of hitting the center of the target on each shot. We want to design a simulation to estimate the probability that Quinn stays in the competition for at least 10shots. Describe how you would use each of the following chance devices to perform one trial of the simulation.

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Superpowers A random sample of 415children from England and the United States who completed a survey in a recent year was selected. Each student鈥檚 country of origin was recorded along with which superpower they would most like to have: the ability to fly, ability to freeze time, invisibility, superstrength, or telepathy (ability to read minds). The data are summarized in the two-way table.

Suppose we randomly select one of these students. Define events E: England, T: telepathy,

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b. The student is not a sixth-grader and did not rate good grades as important.

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30%and 10%of the parts, respectively. Historical records indicate that 10%of the parts

produced by Machine A are defective, compared with 30%for Machine B, and 40%for

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