MathCounts Help

Q: In 2010, the probability of Mark sinking a free throw was twice what it was in 2009, and yet the probability of him sinking exactly two out of three free throws was the same in both years. What was the probability of Mark sinking a free throw in 2010 given that the probability was greater than zero? Express your answer as a common fraction. A: 6/7

Q: Circle O has a radius of 10 units . Point P is on radius OQ and OP = 6 units. How many different chords containing P, including the diameter, have integer lengths? A: 8

Q: Bob and Tom each roll two standard six-sided dice. What is the probability that the product of their individual sums is greater than 100? Express your answer as a common fraction. A: 35/1296

Q: If  x/2 + y/3 = 1 and x/4 + 2y/3 = -1, what is the value of the sum of x and y? A: 1

Q: What is the probability that a list of five different, single-digit numbers, whose sum is 31, will contain exactly two prime numbers? Express your answer as a common fraction. A: 3/5

Q: Three real numbers a, b, and c satisfy the equations: a + b + c = 2, ab + ac + bc = -7 and abc = -14. Express your answer in simplest radical form. A: √7