1) S'pose we flip 2 fair coins, and roll one fair 6 sided die. What is the probability that the number of heads equals the number showing on the die?
2) We roll 4 fair six sided dice. What is the conditional prob. that the first die shows 2, conditional on the event that at LEAST 3 dice show 2.
P(A|B) = P(A and B)/ P(B)
The Attempt at a Solution
1) 0.25 / (1/3) = 3/4. Is this correct? I have my doubts. :|
EDIT: Now I think it is: (1/3) / 0.75 = 4/9
2) The first of the question asks, if "EXACTLY" 3 dice show 2, in which the answer is 3/4. But for at least 3 show 2, I don't get how to mathematically show it, using the above formula. Intuitively I understand that the prob. has to be greater than 3/4 in this case, just don't know how to show. Any help would be appreciated.