Sample space?

Question

There are teo boxes. One with 6 balls number 1-6 and one with seven numbered 1-7. If they are thoroughly shaken and ball is drawn from each, what is the probability that
(a) Both will be 1's
(b) Exactly one of the will be a 2
(c) Both will be even
(d) Exactly one of them will be even?

I am confused with the no of sample space. Howmany elements are there in the sample space?

Answer 1

The sample space consists of all pairs (x,y) with 1 <= x <= 6 and 1 <= y <= 7. There are 6 * 7 = 42 in elements and each is equally probable. You only need to count up the number of elements in each event (subset of the sample space) and divide by 42 to get the answers:

(a) 1 (1,1) --> P = 1/42
(b) 6 (2,x)'s + 5 (x,2)'s --> P = 11/42
(c) 9 (even,even)'s --> P = 9/42
(d) 12 (even,odd)'s + 9 (odd,even)'s --> P = 21/42 = 1/2

Answer 2

there are six elements in the sample sapce for the first and seven in the second.
you cant use conditional probability with one sample space because the events are independant. ie: the probability of choosing any one ball from the one box does not change no matter what you do to the second. you have to therefore treat them as two seperate experiments.