Chapter 8, Problem 16PS

(a)

To determine

To calculate: The expected value $V$, given that from numbers $1$ to $47$ five different numbers are chosen and the MEGA number chosen from the numbers $1$ to $27$ must match to win California’s Super Lotto Plus Game. The cost of purchasing the ticket is $\text{\$}1$ and the amount of winning is $\$12,000,000$. Also, it is given that the expected value $V$ can be calculated as the sum of the products of the $n$ possible outcomes of an event and the probabilities of $n$ outcomes to occur.

$V=P_1{x}_1+P_2{x}_2+\dots +P_n{x}_n$

Where, $x_1,x_2,x_3,\dots ,x_n$ are the values of $n$ possible outcomes of an event and $P_1,P_2,P_3,\dots ,P_n$ are the probabilities of the $n$ outcomes to occur.

(b)

To determine

To calculate: The expected value $V$ of each turn, if the game is of rolling two six-side dice. The score for the turn is the product of the numbers on the dice when the numbers on both the dice is same otherwise, it is $0$. Also, calculate the number of turns required to make a score of $60$ points.