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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.Should you play the game?

Short Answer

Expert verified

The value of excepted value is positive ,so we should play the game.

Step by step solution

01

Calculation for probability

Calculate probability:

There are 52cards.

The no of facing card is12.

So,

If the card is face card,

localid="1649793593859" 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)=totalnooffacingcardtotalnoofcards

4052

=0.769

The values are shown in following table.

02

Calculation of expected value and needed of game

The value for expected is,

μ=0.231×30-2×0.769

=6.93-1.538

=5.392

The value of expected is positive.

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