Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

You are presented with a deck of $10$ cards, numbered from $1$ to $10$ and can draw one card. If the number is odd, you win $\$13$ . If the number is even, you win nothing. If you play the game, what is the expected payoff? $\newline$ $\$$ ____

View step-by-step help

View step-by-step help

Expected values for a game of chance

Full solution

Q. You are presented with a deck of

10

cards, numbered from

1

to

10

and can draw one card. If the number is odd, you win

\$13

. If the number is even, you win nothing. If you play the game, what is the expected payoff?

\newline

\$

____

Calculate odd number probability: Calculate the probability of drawing an odd number. $\newline$ Number of odd cards: $5$ ( $1$ , $3$ , $5$ , $7$ , $9$ ) $\newline$ Total number of cards: $10$ $\newline$ Probability of odd number $=$ Number of odd cards $/$ Total number of cards $\newline$ Probability of odd number $=$ $1$ $0$ $\newline$ Probability of odd number $=$ $1$ $2$
Calculate even number probability: Calculate the probability of drawing an even number. $\newline$ Number of even cards: $5$ ( $2$ , $4$ , $6$ , $8$ , $10$ ) $\newline$ Total number of cards: $10$ $\newline$ Probability of even number $=$ Number of even cards $/$ Total number of cards $\newline$ Probability of even number $=$ $2$ $0$ $\newline$ Probability of even number $=$ $2$ $2$
Calculate expected payoff for odd number: Calculate the expected payoff for drawing an odd number. $\newline$ Probability of odd number = $0.5$ $\newline$ Amount won for odd number = $\$13$ $\newline$ Expected payoff for odd number = Probability of odd number $\times$ Amount won for odd number $\newline$ Expected payoff for odd number = $0.5 \times 13$ $\newline$ Expected payoff for odd number = $6.5$
Calculate expected payoff for even number: Calculate the expected payoff for drawing an even number. $\newline$ Probability of even number = $0.5$ $\newline$ Amount won for even number = $\$0$ $\newline$ Expected payoff for even number = Probability of even number $\times$ Amount won for even number $\newline$ Expected payoff for even number = $0.5 \times 0$ $\newline$ Expected payoff for even number = $0$
Calculate total expected payoff: Add the expected payoffs for odd and even numbers to get the total expected payoff. $\newline$ Total expected payoff = Expected payoff for odd number + Expected payoff for even number $\newline$ Total expected payoff = $6.5 + 0$ $\newline$ Total expected payoff = $6.5$

More problems from Expected values for a game of chance

Question

A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.

\newline

If the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

Posted 1 month ago

Question

There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____

Posted 3 months ago

Question

There are two different raffles you can enter.

\newline

In raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are

1,000

in the raffle, each costing `$11`.

\newline

Raffle B is for a `$370` prize. Out of

125

tickets, each costing `$5`, one ticket will win the prize, and the other tickets will win nothing.

\newline

Which raffle is a better deal?

\newline

\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

Posted 2 months ago

Question

X

is a normally distributed random variable with mean

49

and standard deviation

25

\newline

What is the probability that

X

24

74

?

\newline

0.68-0.95-0.997

rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

\newline

Posted 3 months ago

Question

X

is a normally distributed random variable with mean

65

and standard deviation

8

\newline

What is the probability that

X

62

68

?

\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

Posted 3 months ago

Question

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

43

and standard deviation

3

30\%

of the values are those less than ______.

Posted 3 months ago

Question

Y

is the number of desserts available in a randomly chosen restaurant.

\newline

Is the random variable

Y

discrete or continuous?

\newline

\newline

\text{[A]discrete}

\newline

\text{[B]continuous}

Posted 3 months ago

Question

Which of the following functions are continuous for all real numbers?

\newline

g(x)=\ln (x)

\newline

f(x)=\frac{1}{x}

\newline

1

\newline

g

\newline

f

\newline

g

f

\newline

g

f

Posted 3 months ago

Question

Which of the following functions are continuous at

x=-1

\newline

g(x)=\sin (x+1)

\newline

f(x)=\frac{1}{x-1}

\newline

1

\newline

g

\newline

f

\newline

g

f

\newline

g

f

Posted 2 months ago

Question

g

be a continuous function on the closed interval

[-1,4]

g(-1)=-4

g(4)=1

\newline

Which of the following is guaranteed by the Intermediate Value Theorem?

\newline

1

\newline

g(c)=-3

for at least one

c

-1

4

\newline

g(c)=3

for at least one

c

-4

1

\newline

g(c)=-3

for at least one

c

-4

1

\newline

g(c)=3

for at least one

c

-1

4

Posted 2 months ago