Question

Ten fair six-sided dice are rolled. The expected value of the product determined by these dice rolls is about 276,000. Can you infer that the probability of obtaining a product lesser than the EV is close to 50%? Why or why not?

Answer 1

Since each of the dice is fair and so we have equal chance of obtaining all the 6 possible values.

So, the distribution is uniform. The expected value on each of the dice is = (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5.

The probability of obtaining a value if 3.5 or less in each of the dice is 0.5.

Now the expected value of product determined by 10 rolls is = = 276000 (approximately).

So, the probability of obtaining a product less than the expected value = = 0.00098.

So, the probability is not close to 50%.