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

There is a spinner with 20 equally likely sections, numbered from 1 to 20. You have the opportunity to spin it. If the number is odd, you win $28. If the number is even, you win nothing. If you play the game, what is the expected payoff?

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question

In a raffle, one ticket will win a $730 prize, and the other tickets will win nothing. There are 200 in the raffle. If you have a ticket, 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 raffle. Call it

Since the only prize is $730, the values

can take are $730 and $0 (if no prize is won).

Since 1 ticket has a payoff of $730, the probability of winning $730 is

200

0.005

That is,

730)

0.005

Since the 199 remaining tickets have a payoff of $0, the probability of winning $0 is

199

200

0.995

That is,

0.995

Write the probability distribution of

in the table.

X	P ( X )
$0	0.995
$730	0.005

To find

(

)

the expected value of

find

(

)

for each value

that

can take. Then, sum these terms.

X	P ( X )	X P ( X )
$0	0.995	$0
$730	0.005	$3.65

(

)

3.65

$3.65

The expected payoff is $3.65.

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

DD.5Expected values of random variables

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