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Chapter 4: Q. 35 (page 285)

You are playing a game by drawing a card from a standard deck and replacing it.If the card is face card, you win \(30.If it is not face card,you pay \)2.There are 12face card in a deck of 52cards.What is the expected value of playing game?

Short Answer

Expert verified

The expected value of playing game is5.392.

Step by step solution

01

Calculation of probabilities

Calculate probability:

There are 52cards.

The no of facing card is12.

So,

If the card is face card,

P(x)=totalnooffacingcardtotalnoofcards

P(x)=1252

=0.231

If the card is not facing card,

Number of not facing card is 40.

So,

P(x)=totalnoofnotfacingcardtotalnoofcards

=4052

=0.769

The values are shown in following table.

02

Calculation for expected value

The value for expected is,

渭=0.231脳30-2脳0.769

=6.93-1.538

=5.392

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