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.
A: ?
You got (a) correct. So, for (b), just plug in x=5 and evaluate the fraction.
Thank you so much! So the correct answer is 15/76 or 0.20?
Please, will you help me with my other posts as well?
Am I correct?
you are correct
the answer for a is x(x+10)/ (2x+10) (2x+9)
the answer for b is 0.20
To find the probability, we need to substitute the value of x in the expression with the given number of black tiles. In this case, we are given that there are 5 black tiles in the bag.
a. The expression that represents the probability of Rachel picking a black tile, then a white tile is:
P(black, then white) = x(x + 10) / (2x + 10)(2x + 9)
Substituting x with 5 (number of black tiles):
P(black, then white) = 5(5 + 10) / (2 * 5 + 10)(2 * 5 + 9)
= 75 / 140
= 0.54
Therefore, the probability that Rachel will pick a black tile, then a white tile is approximately 0.54.
b. With 5 black tiles in the bag, we can use the expression from part a to calculate the probability.
P(black, then white) = 5(5 + 10) / (2 * 5 + 10)(2 * 5 + 9)
= 75 / (20)(19)
= 0.197
Rounding to the nearest hundredth, the probability that Rachel will pull a black tile, then a white tile with 5 black tiles in the bag is approximately 0.20.