Question

Please explain!
Joseph played a game at the fair. He had to take out 2 balls from a bag of 50 balls. There were red and black balls in the bag. Both the balls he picked were black. The man running the stall said: 'There was a 4/175 chance that you would do that.' What is the number of red balls
that were in the bag at the start?

A 46
B 42
C 38
D 34

Many thanks

Answer 1

number of black --- x
number of red ----- 50-x

prob(2 black) = (x/50)(x-1)/49 = 4/175
(x^2 - x)/2450 = 4/175
175x^2 - 175x = 9800
divide by 25
7x^2 - 7x - 392 = 0
(x - 8)(7x + 49) = 0
x = 8 or x = -49, can't have negative number of balls

There were 8 black balls and 42 red balls

check: prob (2 black)
= (8/50)(7/49) = 4/175 , as stated in problem