Question

For a multistate​ lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts​ (a) through​ (c) below. x​ (cash prize,​ $) ​P(x) ​200,000 ​10,000 100 7 4 3 0 ​(a) If the grand prize is ​$​, find and interpret the expected cash prize. If a ticket costs​ $1, what is your expected profit from one​ ticket

Answer 1

According to the distribution, we have that:

• The expected cash price is of $0.1165, which means that if a person plays the game many times, on average, the cash price earned would be of $0.1165 per game.

• The expected profit from one ticket is of -$0.8835.

The probability distribution for the prizes is given by:

$P(X = 200,000) = 0.00000000764$

$P(X = 10,000) = 0.00000019$

$P(X = 100) = 0.000001787$

$P(X = 7) = 0.004859191$

$P(X = 4) = 0.006351519$

$P(X = 3) = 0.01781606$

$P(X = 0) = 0.97082745836$

The expected cash price is given by the sum of each outcome multiplied by it's probability, thus:

$E(X) = 0.00000000764(200000) + 0.00000019(10000) + 0.000001787(100) + 0.004859191(7) + 0.006351519(4) + 0.01781606(3) + 0.97082745836(0) = 0.1165$

The expected cash price is of $0.1165, which means that if a person plays the game many times, on average, the cash price earned would be of $0.1165 per game.

The profit is the expected cash price subtracted by the cost, thus:

$P = 0.1165 - 1 = -0.8835$

The expected profit from one ticket is of -$0.8835.

A similar problem is given at https://brainly.com/question/24855677