Question

You play a game using fair dice and fair coins. First you flip 72 coins. For each coin that is a heads, you roll 5 six-sided dice. You sum all the six-sided dice you roll to calculate your total score. What is the expected total score from this game

Answer 1

630

Explanation:

Given that:

First flip = 72 coins

For each coin which is a head, you roll = 5, six-sided dice

Thus, the expected sum on a single six-sided dice =
`\sum x P(x)`

`\sum x P(x)` =
`(1)/(6)* (1+2+3+4+5+6)`

`\sum x P(x)` = 3.5

Thus, the expected sum on the five six-sided dice = 5 × 3.5 = 17.5

However, for a single flip :

The expected sum = P(heads) × expected sum on 5 dice + P(tails) × expected sum on 0 dice.

Expected sum =
`(1)/(2) * 17.5 + (1)/(2) * 0`

Expected sum = 8.75

Hence, the expected total score from this game = 72 × 8.75 = 630