Question

A card is drawn at random from a standard deck of playing cards (no jokers). If the card is a spade, the player wins $7; if it is not a spade, the player loses $1.

What is the expected value of this game? $________________

Answer 1

The expected value of the game is the mean value of the game

The expected value of the game is $1

How to determine the expected value?

There are 13 spades in a deck of card of 52

So, the probability of selecting a spade is:

P(Spade) = 13/52

Simplify

P(Spade) = 1/4

Winning = $7

The probability of not selecting a spade is:

P(Not spade) = 1 - 1/4

Simplify

P(Not spade) = 3/4

Lose = $1

The expected value of the game is:

$E(x) = \sum x * P(x)$

This gives

$E(x) = \frac 14 * 7 - 1 * \frac34$

Simplify

$E(x) = \frac 74 - \frac34$

Evaluate

$E(x) = 1$

Hence, the expected value of the game is $1

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