Question

Suppose your state lottery has an expected value of
−34%.
If you spend $40 per month on lottery tickets, how much money would you be expected to lose in an average year?
We can expect to lose $
.

Answer 1

Answer:

$163.20

Step-by-step explanation:

Your state lottery has an expected value of −34%.

You spend $40 per month on lottery tickets. So, you can expect to lose 34% of the amount you spend.

Find 34% of $40:

$\ 40\cdot 0.34=\ 13.60$

Hence, we can expect to lose $13.60 per month.

A year (12 months period) expected lose is

$\ 13.60\cdot 12=\ 163.20$

Answer 2

The money that you would be expecting to lose in an average year is $163.2

How to find expected value of sum of random variables?

Suppose that the random variable in consideration be X, and its expectation is given by E(X).

Then, if we take another random variable Y = X + X + .. +X (n times) = n X

Then, we get: $E(Y) = nE(X)$

For the given case, let we take two random variables X and Y, such that:

X = Amount won in lottery if $40 is invested

E(X) = -34% of $40 = $\dfrac{40}{100} \times -34 =- 13.6 \: \text{(in dollars)}$ = -$13.6 (this shows that amount won was negative, or $13.6 dollars lost).

Y = Amount earned in an year = 12 times sum of X's value for each month (As 1 year = 12 month) if each month $40 was invested.

Then, we get

E(Y) = Expected amount won averagely in an year

$Y = 12 \times X\\E(Y) = E(12 \times X) = 12 \times E(X) = 12 \time -13.6 = -163.2 \: \text{(in dollars)}$

(negative sign shows that opposite of "won" occurred, which is "lost" )

Thus, the money that you would be expecting to lose in an average year is $163.2

Learn more about expectation of a random variable here:

https://brainly.com/question/4515179