SOLUTION: An urn contains 7 red, 5 blue, and 3 white marbles. You draw three marbles randomly without replacement. If the random variable R is defined to be the number of red marbles drawn,

Algebra ->  Probability-and-statistics -> SOLUTION: An urn contains 7 red, 5 blue, and 3 white marbles. You draw three marbles randomly without replacement. If the random variable R is defined to be the number of red marbles drawn,       Log On


   

Question 946282: An urn contains 7 red, 5 blue, and 3 white marbles. You draw three marbles randomly without replacement. If the random variable R is defined to be the number of red marbles drawn, what is the expected value of R?
Answer by mathmate(429) About Me  (Show Source):
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Given
Urn contains 7 red, 5 blue and 3 white marbles for a total of 15.
Three are drawn without replacement.
Find expected number of marbles drawn.

Solution
First we will need to find the probabilities of drawing 0, 1, 2 and 3 marbles.
P(0) = 8%2F15%2A7%2F14%2A6%2F13+=+8%2F65+
P(1) = 3%2A%287%2F15%2A8%2F14%2A7%2F13%29+=+28%2F65+%29
P(2) = 3%2A%287%2F15%2A6%2F14%2A8%2F13%29+=+24%2F65+
P(3) = 7%2F15%2A6%2F14%2A5%2F13+=+5%2F65+
Check: P(0)+P(1)+P(2)+P(3) = 1, checks.

Next we will calculate the expected value of X = number of reds.
E[X] = Σ x*P(x) = 0%2A%288%2F65%29%2B1%2A%2828%2F65%29%2B2%2A%2824%2F65%29%2B3%2A%285%2F65%29+=+7%2F5+=+1.4


Answer
The expected number of red marbles drawn is 1.4