a. P(odd sum)
OK, each is drawing from a pile of 2 even cards and one odd, so have a 2/3 chance of picking even and a 1/3 chance of picking odd.
1/3 × 1/3 = 1/9 probability of odd+odd = even
1/3 × 2/3 = 2/9 prob of odd + even = odd
2/3 × 1/3 = 2/9 prob of even + odd = odd
2/3 × 2/3 = 4/9 prob of even+even = even
Total odd: 2/9+2/9 = 4/9
Answer: a) 4/9
b. P(sum < 11)
Let's just work out all the possibilities and count.
1st 2nd sum
4 4 8
4 5 9
4 6 10
5 4 9
5 5 10
5 6 11
6 4 10
6 5 11
6 6 12
I count 6 of 9 are less than 11, so P=6/9 or
Answer: b) 2/3
