IXL - Expected values for a game of chance (Algebra 2 practice)

For a fundraiser, there is a raffle with 250 tickets. One ticket will win a $490 prize, and the remaining tickets will win nothing. If you have a ticket, what is the expected payoff?

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question

A game show host is going to draw a random number from 1 to 10. If the number is even, you win $22. If the number is odd, you win nothing. If you play the game, what is the expected payoff?

key idea

A random variable is a function that assigns a numerical value to each outcome in a sample space. Note that though random variables are functions, they are usually denoted by capital letters like

is a random variable,

(

)

is the probability that

takes the value

The function that maps

(

)

is the probability distribution of

A probability distribution is frequently represented as an equation, table, or graph.

The expected value or mean

(

)

of a random variable

is the sum of the terms

(

)

for each value

that

can take. It is also called the expected value or mean of the probability distribution of

and is sometimes written

𝜇

solution

Use the random variable whose value is the payoff in the game. Call it

Since the only prize is $22, the values

can take are $22 and $0 (if no prize is won).

Notice that half of the possible numbers are odd and half are even, so

22) and

0) are both

0.5

Write the probability distribution of

in the table.

X	P ( X )
$0	0.5
$22	0.5

To find

(

)

the expected value of

find

(

)

for each value

that

can take. Then, sum these terms.

X	P ( X )	X P ( X )
$0	0.5	$0
$22	0.5	$11

(

)

$11

The expected payoff is $11.

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PP.8Write the probability distribution for a game of chance

PP.5Expected values of random variables

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