Answer :

Given : Four rotten oranges are mixed with 16 good ones. Three oranges are drawn one by one without replacement.

To find : mean (๐) and variance (ฯ^{2})

Formula used :

Mean = E(X) =

Variance = E(X^{2}) -

Mean = E(X) = = x_{1}P(x_{1}) + x_{2}P(x_{2}) + x_{3}P(x_{3})

Four rotten oranges are mixed with 16 good ones. Three oranges are drawn one by one without replacement.

Let X denote the number of rotten oranges drawn

There are 4 rotten oranges present in 20 oranges

P(0) = = =

P(1) = = =

P(2) = = =

P(3) = = =

The probability distribution table is as follows,

Mean = E(X) = 0() + 1() + 2() + 3() = 0 + + + =

Mean = E(X) = =

= =

E(X^{2}) = = P(x_{1}) + P(x_{2}) + P(x_{3})

E(X^{2}) = () + () + () + () = 0 + + + =

E(X^{2}) = =

Variance = E(X^{2}) - = โ = =

Variance = E(X^{2}) - =

Mean = E(X) =

Variance =

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