While playing a game, Rachel pulls two tiles out of a bag without looking and without replacing the first tile. The bag has two colors of tiles--black and white. There are 10 more white tiles than black tiles.
a. Write and simplify an expression that represents the probability that Rachel will pick a black tile, then a white tile.
A: x(x + 10)/(2x + 10)(2x + 9)
b. What is the probability that Rachel pulls a black tile and then a white tile if there are 5 black tiles in the bag berfore her first pick? Round your answer to the nearest hundredth
im having trouble on figuring out the steps to solve b.
a) is correct, but you should have brackets around the complete denominator. The way you typed it, it is only divided by (2x+10)
x(x + 10)/( (2x + 10)(2x + 9) )
b) So now we have an actual numerical case
and let's just follow the same argument you did in a)
blacks = 5
whites = 15
prob(black, then white) = (5/20)(15/19)
= 75/380
= 15/76
number or blacks = b
number of whites = b+10
total - b +b+10 = 2 b+10
black first
b/(2b+10)
now we have b-1 blacks
we have b+10 whites still
total = 2b+9
b/(2b+10) * (b+10)/(2b+9)
note - not 2b+10 in numerator
sorry, read reply wrong. You have it fine
To solve part b, we need to substitute the value of x into the expression from part a and simplify.
Given that there are 5 black tiles in the bag before Rachel's first pick, we substitute x = 5 into the expression:
Probability = (x(x + 10))/(2x + 10)(2x + 9)
= (5(5 + 10))/(2(5) + 10)(2(5) + 9)
= (5(15))/(20)(19)
= 75/380
≈ 0.197
Therefore, the probability that Rachel pulls a black tile, then a white tile, given there are 5 black tiles in the bag before her first pick, is approximately 0.197.