Question

• gamble #1: flip a coin, and earn $70 if heads (probability 0.5) and $0 if tails (probability 0.5). • gamble #2: roll a die (which will come up as 1, 2, 3, 4, 5, or 6, with each outcome having probability 1/6) and earn $10 times the number on the die.

Answer 1

On average, gamble #1 will net you


`0.5\cdot70+0.5\cdot0=35`

dollars per coin toss, while gamble #2 would yield


`\frac{10}6+\frac{20}6+\cdots+\frac{60}6=\frac{10}6\cdot\frac{6\cdot7}2=35`

dollars per roll of the die. But in every outcome of the second gamble, you're guaranteed to win some amount of money, so you should probably choose that, assuming the question is which you should choose to play.