Expert: Josh - 3/10/2007

Question
three dice and three coins are tossed, what is the probabiltiy that the coins will all be the same and the dice will all be the same?

Answer
Hi Michelle,

Let's look at these one by one. When we toss each coin, there are two possible outcomes (either "head" or "tail"). When two coins are tossed independently, we have 2x2=4 possible outcomes. These are {HH, HT, TH, TT}. The probability of getting the same face is 2/4.
Extending this argument, when three coins are tossed, there are 2x2x2=8 possible outcomes. These are {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. The probability of getting the same face in all three coins is 3/8.

For the dice, each one has 6 possible outcomes. Thus, the three dies produce 6x6x6=216 outcomes; from which we are only interested in "1,1,1", "2,2,2", "3,3,3", "4,4,4", "5,5,5" and "6,6,6". The probability of getting these is 6/216 or 1/36.

The joint probability where the coins will all be the same and the dice will all be the same is given by (3/8)x(1/36) or 1/96