You have 7 Red Marbles, 2 Green Marbles, and they are combined in a bag. You pick 3 marbles out of the bag. What is the probability that 2 of the 3 are green?
((2/9)^3) * 2/3 = .00732 which is incorrect.
Correct answers are:
.0833
.0022
.4286
Mitch
Favorite Answer
For this problem, use the Hypergeometric Probability Formula:
P(x) = [(sCx)*(N-sCn-x)] / NCn
where:
N = is the size of the population (9)
s = is the number of successes in the population (2)
x = is the number of successes in the sample (2)
n = is the size of the sample or the number of trials (3)
C = is the symbol for a Combination
P(x) = [(sCx) * (N-sCn-x)] / NCn
P(2) = [(2C2) * (9-2C3-2)] / 9C3
P(2) = [(2C2) * (7C1)] / 9C3
P(2) = [(1) * (7)] / 84
P(2) = [7] / 84 = 1/12 or 0.0833
Yeah, the math gets really messy,
but you can use an online Hypergeometric Probability Calculator:
http://stattrek.com/Tables/Hypergeometric.aspx
To answer an earlier question, there's no built in function for the TI-83/84,
but this is as close as it gets:
http://mathbits.com/MathBits/TISection/Statistics2/bernoulli.htm
Good luck in your studies,
~ Mitch ~
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Marble Probability Calculator
Daniel
what is the probability of green being chosen if there is 9 red marbles 6 blue marbles 7 green marbles 11 yellow marbles