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.

$\"\\\\P(winning)=\\frac{Number\\$

$\"\\\\P(Fail)=\\1-P(winning)\\\\$

Step 2:

If he loose the game than he loose $ 2.

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

Expected value $\"E(X)=\\sum$ .

$\"\\\\E(X)=(2)P(winning)+(-2)P(Fail)\\\\$

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.

$\"\\\\\\mu=n\\times$