Question

Uppose you select a random card from a standard deck of

52

cards and no jokers. If you draw a face card (king, queen, or jack), you win

$5

. If you draw an ace, you win

$20

. If you draw any other card, you lose

$2

. What is the expected profit from any one draw?

Answer 1

The value is
`E(k) = (68)/(52)`

Explanation:

From the question we are told that

The total number of cards is
`n = 52`

Let k represent the winnings and loss when any card is drawn

So k = $5 when a faced card is drawn

So k= $ 20 when an Ace card is drawn

So g = - $2 when any other card is drawn

Generally in a standard deck of card

The number of Ace is 4

The number of queen is 4

The number of jack is 4

Therefore the number off faced cards is

R = 4 + 4 + 4 = 12

Generally the number of other cards is

Y = n - R

=> Y = 52 - 12

=> Y = 36

Generally the probability of drawing a faced card is mathematically represented as

`P(k = 5) = ( 12)/(52)`

Generally the probability of drawing a Ace card is mathematically represented as

`P(k = 20) = ( 20)/(52)`

Generally the probability of drawing a other card is mathematically represented as

`P(k = -2) = ( 36)/(52)`

Generally the expected profit from any one draw is mathematically represented as

`E(k) = \sum k_i * P(K = k)`

=>
`E(k) =  5 * ( 12)/(52)  + 20( 20)/(52) + [- 2 * ( 36)/(52)]`

=>
`E(k) = (68)/(52)`