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15) Support you pay $2.00 to roll a fair die with the understanding that you will get back $4.00 for rolling a 2 and 3, nothing otherwise . What is your expected value?

21) The probability of winning a certain lottery is 1/70,422. For people who play 545 times, find the mean number of wins.

asked Mar 18, 2015 in STATISTICS by doan12345 Pupil

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2 Answers

Step 1:

To play rolling fair die game one need to pay $ 2.

Roll a die, if one get 2 or 3 than he win the game.

If he win the game, he will get back $ 4.

A fair die has 6 faces.

Find the probability of getting 2 or 3.

$\\P(winning)=\frac{Number\ of \ favorable \ events }{Total\ events}\\\\ P(winning)=\frac{2 }{6}\\\\ P(winning)=\frac{1}{3}$

$\\P(Fail)=\1-P(winning)\\ \\P(Fail)=\1-\frac{1}{3}\\ \\P(Fail)=\frac{2}{3}\\$

Step 2:

If he loose the game than he loose $ 2.

If he won the game than he will got $ 2. (Since in the beginning he pay $2 to play so => 4 - 2 = 2)

Expected value $E(X)=\sum x.P(X=x)$ .

$\\E(X)=(2)P(winning)+(-2)P(Fail)\\ \\E(X)=(2)\frac{1}{3}-2\frac{2}{3}\\ \\E(X)=\frac{2}{3}-\frac{4}{3}\\ \\E(X)=-\frac{2}{3}\\ \\E(X)=-0.67\\$

Solution :

The expected value is -0.67.

answered Mar 18, 2015 by yamin_math Mentor

(21)

Step 1:

The probability of winning a lottery is $\frac{1}{70422}$ .

Assume that a procedure yields a binomial distribution with a trial repeated n times.

Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

n = 545, $p=\frac{1}{70422}$ .

binomial mean = n * p.

$\\\mu=n\times p\\ \\\mu=545\times \frac{1}{70422}\\ \\\mu=0.0077$

Solution :

Mean number of wins is 0.0077.

answered Mar 18, 2015 by yamin_math Mentor

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