Chapter 17, Problem 60E

An honest die is rolled. If the roll comes out even $\left(2,4,\text{or }6\right)$ you will win $\$1$; if the roll comes out odd $\left(1,3,\text{or 5}\right)$, you will lose $\$1$. Suppose that in one evening you play this game $n=2500$ times in a row.

a. Estimate the probability that by the end of the evening you will not have lost any money.

b. Estimate the probability that the number of “even rolls” $\left(\text{roll a }2,4,\text{or }6\right)$ will fall between 1250 and 1300.

c. Estimate the probability that you will win $\$100$ or more.