Question

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn't possible for a die to turn up with a value of 3.5, the expected value couldn't possibly be 3.5. Who is right

Answer 1

Answer:

Helene is right

Step-by-step explanation:

Mathematically, the expected values is defined as the sum of all the possible outcomes that an event can have times the probality of the respective outcome:

x = ∑ p *i,

where x is the expected value, i represents every outcome that can occur, and p is the probability of said outcome.

Now, for the case of a dice, the expected value would be:

x = 1 * $\frac{1}{6}$ + 2 * $\frac{1}{6}$ + 3 * $\frac{1}{6}$ + 4 * $\frac{1}{6}$ + 5* $\frac{1}{6}$ + 6 * $\frac{1}{6}$,

as every outcome has the same chance of happenning. Solving we get that:

x= $\frac{1}{6}$ *(1 +2 +3 +4+5+6) = $\frac{1}{6}$ * 21 = 3.5

Helene is right.