Dan rolls a fair dice 24 times.
How many times would Dan expect to roll an even number?

Assuming a fair, six sided die, 4 would be expected to come up in one sixth of the trials, so 4 times in 24 rolls.

More formally:

Let X be the number of 4s rolled in 24 independent rolls of a fair six sided die. X is then distributed binomially with parameters n and p.

p = Probability of rolling a 4 = 1/6

n = Number of trials = 24

E [X] = np (by the properties of Binomial distribution)

E [X] = 4

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