On three rolls of a single die, you will lose $19 if a 3 turns up at least once, and you will win $5 otherwise. what is the expected value of the game?
let x be the random variable for the amount won on a single play of this game.

It is expected to lose 5.10 dollars

Step-by-step explanation:

The probability of getting a 3 by throwing a die once is 1/6.

By throwing it 3 times the probability of not getting a 3 is:

Then the probability of obtaining a three at least once in the 3 attempts is:

So if X is the discrete random variable that represents the amount gained in a single move of this game, the expected gain E(X) is:

-16 cents

Step-by-step explanation:

We are given that on  three rolls of a single die, you will lose $19 if a 3 turns up at least once, and you will win $5 otherwise.

We are to find the expected value of the game.

P (at least one 5 in three rolls) = 1 - P (no. of 3 in three) = = 0.875

P (other results) = 1 - 0.875 = 0.125

Random game value = -19, +5

Probabilities: 0.875, 0.125

Expected game value (X) = 0.875 × (-19) + 0.125 × (5) = -16 cents

Therefore, every time you play the game, you can expect to lose 16 cents

d. (18.7)

Step-by-step explanation:

The formula for the law of sines in order to find m^2

This equation was derived because:

m=the side you are finding

j=side that is adjacent to M, the angle with side m as its opposite

k=side that is also adjacent to M

In short,

(The opposite side of angle)^2=(Adjacent side of angle)^2 + (The other adjacent side of angle)^2 - (the adjacent side) (the other adjacent side