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kipiarov [429]
3 years ago
14

Consider the following game: Roll a fair 6-sided die. You win if the result is greater than 4; otherwise, you lose. To play, you

must pay $4. If you win, you get $8; if you lose, the $4 fee is forfeited. What is the expected value for the amount gained/lost
Mathematics
1 answer:
dalvyx [7]3 years ago
4 0

Answer:

-$1.33 or lose $1.33

Step-by-step explanation:

In this game, there are two possible outcomes.

- There is a 2 in 6 chance (rolling a 5 or a 6) that you win $8.

- There is a 4 in 6 chance (rolling a 1, 2, 3 or a 4) that you win nothing.

Note that for any outcome, you start off paying $4 to play.

The expected value of this game is:

E(X) =\frac{2}{6} *\$8+\frac{4}{6}*\$0-\$4\\E(X) = -\$1.33

You are expected to lose $1.33 per play.

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8. Loren already knows that he will have $500,000 when he retires. If he sets up a payout
Ulleksa [173]

The annuity could provide $221.19 each month

Step-by-step explanation:

The ANNUITY FORMULA is P_{t}=\frac{d[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}} , where

1. P_{t} is the balance in the account after t years

2. d is the regular deposit (the amount you deposit each year or month

    or .........)

3. r is the annual interest rate in decimal

4. n is the number of compounding periods in one year

5. t the number of years

∵ Loren knows that he will have $500,000 when he retires

∴ P_{t} = $500,000

∵ he sets up a payout  annuity for 30 years in an account paying 10%

  interest

∴ t = 30 years

∴ r = (10/100) = 0.1

∵ The annuity  could provide each month

∴ n = 12

Substitute the values above in the formula

∴ 500,000=\frac{d[(1+\frac{0.1}{12})^{(12)(30)}-1]}{\frac{0.1}{12}}

∴ 500,000=\frac{d[(1.00833333)^{360}-1]}{0.00833333}

∴ 500,000 = d [2260.487925]

- Divide both sides by 2260.487925

∴ d = $221.19

The annuity could provide $221.19 each month

Learn more:

You can learn more about deposit in brainly.com/question/8782252

#LearnwithBrainly

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