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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—clubs, 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 “face cards.” 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 “heart” and “face card” 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∩B)=P(A)×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∩Y)=332

Now check the required condition as:

P(X∩Y)=P(X)×P(Y)352=14×313352=352

Since, the required condition is satisfied. Thus, it could be said that the events “face card” and “heart” are independent.

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