A Bag contain 5 black 6 white and 7 red balls four balls are drawn at random from it.If x denotes the number of white balls,then findE(x)

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A Bag contain 5 black 6 white and 7 red balls four balls are drawn at random from it.If x denotes the number of white balls,then findE(x)

preetirajuom 25th Jan, 2021

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Answer (1)

ARYAN SAGAR 25th Jan, 2021

Dear student,

Total number of balls in bag = 18 out of which 6 are white balls and other balls count to a total of 12.

It is given that X is the number of the white balls drawn. And the white balls are drawn four in number.
Now, since nothing is given so, we can assume that ball are drawn without replacement.

So, expectation E(X) = summation (XP(X))

So, let P(X=0) = all drawn balls are non-white. So X = 0 so, E ( X = 0) = 0

Now, probability of drawing one white ball, i.e P(X=1) = 4 {(6/18) (12/17) (11/16) (10/15)} = 0.4314
Since we are not told any order so there can be four cases that a White ball is drawn in first attempt or in second attempt or in third attempt or in fourth attempt or you cam saya 4C1 cases.

Now, P( X=2 ) = 6 {(6/18) (5/17) (12/16) (11/15)} = 0.3235

P(X=3) = 4 {(6/18) (5/17) (4/16) (12/15)} = 0.0784

And, P(X=4) = {(6/18) (5/17) (4/16) (3/15)} = 0.0049

So, now E(X) = (1 P(X=1)) + (2 P(X=2)) + (3 P(X=3)) + (4 P(X=4))

So, after calculating the values we get E(X) = 1.3332

Note that expectation is not the probability, so it's value can be also greater than 1.

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