Question:
Calculate the conditional probability that the sum of two dice tosses is even given that at least one of the tosses gives a five.
I'm a bit confused by this. Shouldn't the probability just be 1/2, since we know that at least one of the dice tosses gave us a five, thus the other must give us an odd number?
Best Answer
A = event when one of the tosses gives a five. (Sample space for the conditional probability) Let (n1, n2) represent the outcomes of die1 and die2 A = { (1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (5,1), (5,2), (5,3), (5,4), (5,6) } // (5,5) must be counted once only
Thus n(A) = 11
B = sum of two dice tosses is even n(B|A) = { (1,5), (3,5), (5,5), (5,1), (5,3)|
P(B|A) = n(B|A)/n(A) = 5/11