Question

if two fair dice are rolled, what is the conditional probabilty that the first one lands on 6 given that the sum of the dice is i? compute for all values of i between 2 and 12

Answer 1

what might be the other possible values {1, 2, ..., 5}

so for first slot, you have 1/2

for second slot, you have 5/6

so your probability must be 1/2x5/6

Answer 2

Order matters here (the first one lands on six...) so we just have to check the ways it can happen. For i = 1,2,3,4,5,6 the probability that the first die is six is zero. Can't get those totals if the first die lands on six. For i=7, the probability is 1/6, for i=8, 1/5, ... for i=12, the probability is one.

Answer 3

Said another way, there are six ways to roll a seven, but only one has the first die a six. There are five ways to roll an eight, but only one with the first die a six, and so on.