In a lottery game, a player picks shox numbers from 1 to 20. If the player matches all six numbers, they win 20,000 dollars. Otherwise, they lose $1. What is the expected value of this game? $​

$120ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

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$0.8514 per play.

Step-by-step explanation:

To start solving the problem, we need to understand the definitions of words, the most important of which is "expected value".

Wiki defines expected value as:

"The expected value is also known as the expectation, mathematical expectation, EV, average, mean value, mean, or first moment. More practically, the expected value of a discrete random variable is the probability-weighted average of all possible values."

To mathematically calculate the expected value, we will need to do the sum of the product

x*P(x)

for all possible (outcome) values of x, that is, all values of x for which the probability is non-zero.

Here the possible outcomes are x=-1 (lose) or x=20000 (win)

Total possible number of outcomes = C(24,6) [24 choose 6]

=24!/(6!18!)

= 134596

Out of which there is only one winning combination.

Therefore we conclude:

P(win 20000)=1/134596

P(lose 1)=134595/134596

and hence the expected value is:

20000*(1/134596)+(-1)*(134595/134596)

=-114595/134596

=-0.8514 (rounded to four places after decimal)

Interpretation:

In the long run, if the game is played many, many times, the average loss is $0.8514 per play.

let's first notice, the center of the hyperbola is at the origin, since the focus points are equidistantly 3 units away from the origin, that also means that the distance "c" from the center to either focus is 3.

it should also be notable that, the traverse axis for this hyperbola is vertical, or namely over the y-axis and therefore, the positive fraction will be the one with y-variable.

the traverse "a" component or distance from the center to either vertex is not 2, is more than 2, so we can safely put it at √5 ≈ 2.24.

b and c are the correct answers.

good luck on the quiz! : d