SOLUTION: there are (t) orange balls and 2 yellow balls in a bag. Craig randomly selects one ball from the bag, records his choice and returns the ball to the bag. He then randomly selects

Question 1097130: there are (t) orange balls and 2 yellow balls in a bag. Craig randomly selects one ball from the bag, records his choice and returns the ball to the bag. He then randomly selects a second ball from the bag, records his choice and returns the ball to the bag. It known that the probability that Craig will select two balls of the same colour from the bag is 52%. Calculate how many balls are in the bag
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
The total number of balls in the bag = t + 2
Then probability of selecting two orange balls = P(O) = (t/(t+2))*(t/(t+2)) = (t/(t+2))^2
And the probability of selecting two yellow balls = P(Y) = (2/(t+2))^2
So the total probability of selecting two balls of the same color =
P(O) + P(Y) = t^2/(t+2)^2 + (2/(t+2))^2 = 52/100
Solve for t:
t^2/(t+2)^2 + 4/(t+2)^2 = (t^2+4)/(t+2)^2 = 13/25
This simplifies to
3t^2 - 13t + 12 = 0
and factors as (3t-4)(t-3) = 0
The solutions are t = 4/3, t = 3
There must be an integer number of balls, so t = 3
Thus there are 3 + 2 = 5 balls in the bag
Check:
P(O) + P(Y) = 3/5*3/5 + 2/5*2/5 = 9/25 + 4/25 = 13/25
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