word problem

Question

Rachel pulls two tiles out of a bag of black and white tiles without replacing the first tile. The bag has 10 more black tiles than white tiles. Write and simplify an expression that represents the probability that rRachel pulls two tiles out of a bag of black and white tiles without replacing the first tile. The bag has 10 more black tiles than white tiles. Write and simplify an expression that represents the probability that Rachel will pick a black tile then a white tile. Let x represent the number of white tiles Rachel will pick a black tile then a white tile. Leet x represent the number of white tiles

Answer 1

x= number of white tiles

y = number of black tiles = x + 10

t = total number of tiles = x + y = 2x + 10

t-1 = total number of tiles after one is pulled = 2x + 10 - 1 = 2x + 9

 

P1 = probability of pulling a white tile = x / t = x / (2x + 10)

P2 = probability of pulling a black tile without replacing the first one = y / (t - 1) = (x + 10) / (2x + 9)

 

Pf = probability of the two consecutive events = P1 x P2 = [x / (2x + 10)] x [(x + 10) / (2x + 9)]

Pf = x(x+10) / (2x+10)(2x+9) = (x²+10x) / (4x²+38x+90)