You are given 4 to 1 odds against tossing three tails with three coins, meaning you win $4 if you succeed and you lose $1 if you fail. find the expected value (to you) of the game

-3/8

Step-by-step explanation:

The expected value will be equal to the probability of each of the results multiplied by its earning.

Here we have two possible results: win or lose. So, we need the probability of winning, that is, the probability that tossing three coins I get three tails, and the probability of losing, which will be the probability of getting anything different to three tails.

So, what is the probability of getting three tails?

We toss our first coin, we need to get a tail, The probability, assuming is a fair coin, will be 1/2.

Then we toss the second coin and we need that, having the first being tail, the second also need to be a tail. As the probabilities of both tossings are independent, this is, a tail in the 1st does not affect the probability of having a tail in the 2nd, the probability of having a tail in the second and the first is: (1/2) * (1/2).

Then, as the third coin also is independent to the first two, the probability of getting a tail in the third is: (1/2) * (1/2) * (1/2) = 1/8

So, if the probability of winning is 1/8 and the prize for winning is $4, the expected value of winning is:

EW = 1/8 * 4 = 4/8 = 1/2

Now, we need to do the same with the loses. The probability of losing is automatic, is 1 - probability of winning: 1 - 1/8 = 7/8. This is easy, if I do not win, I lose, and those are to only possible results, so both probabilities need to sum 1 (100%). And if I lose the game I lose $1, so the "prize" is -$1. Thus, the expected value of losing is:

EL = (7/8) * (-1) = -7/8

So, the expected value of the game is the sum of expected values of wining and losing:

ExpectedValue = 1/2 - 7/8 = 4/8 - 7/8 = -3/8

So, the expected value of playing such a game is - $3/8

10.416 meters per second

step-by-step explanation:

distance=1 00 meters

time= 9.6 seconds in decimal form or 9 3/5 as a mixed number

average speed= 100/9.6

=10.416 meters per second or 10 52/125 as a mixed number.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1