Question

Ten cards numbered 1 to 10 are mixed in a hat.Two cards numbered p and q are drawn from the hat.What is the probability that p+q=10?
a) 2/5
b) 4/9
c) 7/45
d) 4/45

Answer 1

a) 2/5b) 4/9
c) 7/45
d) 4/45


Solution.
The total number of all pairs (p,q) from numbers 1..10 is equal to
10 * (10-1) / 2 = 45


Notice that only the following 4 pairs (p,q) has property p+q=10:

1,9
2,8
3,7
4,6

Hence the probability that p+q=10 is equal to
4/45


Answer: d) 4/45