Question

Three dice are rolled and two fair coins are tossed. Let X be the sum of the number of spots that show on the top faces of the dice and the number of coins that land heads up. The expected value of X is ____?

Answer 1

favourable outcome for a digit on dice = 1

and total outcome = 6

So, probability of getting any number of dice = favorable/total = 1/6

Expected value = (sum of numbers)*probability

= (1+2+3+4+5+6)*(1/6)

= 21/6

we have 3 dice, so expected value for 3 dice = 3*E[x]

= 3*21/6

= 63/6

= 10.5

And

Expected value of a single coin = probability of getting heads = 1/2 = 0.5

we have two coins, so expected value of two coins = 2*E[x] = 2*0.5 = 1

therefore, total expected value of X is 10.5+1

E[x_total]= 11.5