Question

Rohan's dad decides to play a game with rohan .Rohan needs to throw a fair die and he will get as much money as the number on the die .For eg if 1 appears on the die the he will get $1, if 2 appears he will get $2 and so on .But if dice turns 6 then he gets $5 and chance to throw dice again.What is the expected amount of money rohan can make ?​

Answer 1

Answer:

4

Step-by-step explanation:

Let expected amount of money Rohan makes is E.

Since he will get $1 for 1, $2 for 2.......$5 for 5 and $5 for 6 plus another throw, we can model the expectation as:

$Prob(X <= 5) = 5/6$

$Prob(X == 6) = 1/6$

$E = E[X <= 5] + E[X == 6]$

$E = \frac{1}{6} * (1 +2 + 3 + 4 + 5) + \frac{1}{6} * (5 + E)$

Solving the above equation for $E$ we get 4