Q. 233.5( 2 Votes )

Four bad oranges

Answer :

4 bad oranges get mixed with 16 hence total oranges are 20.


Now 2 oranges are selected at random from 20 oranges.


Number of ways in which 2 oranges can be selected out of 20 is 20C2


We have to find the probability distribution of number of bad oranges let X be the variable which will represent it.


Now out of the 2 oranges selected none can be bad or 1 can be bad or both.


Hence X can take values 0, 1 and 2


Now let us find the probabilities P (X = 0), P (X = 1) and P(X = 2)


P (X = 0) means probability of getting 0 bad oranges that is both the oranges selected are good


Number of ways in which 2 good oranges can be selected is 16C2 because there are total 16 good oranges out of which 2 are chosen


Hence





P (X = 1) means probability of selecting one bad orange that is one good and one bad orange


Number of ways in which 1 bad orange can be selected out of 4 is 4C1 and number of ways of selecting one good orange out of 16 is 16C1


Hence





P(X = 2) means selecting both the bad oranges


Number of ways in which 2 bad oranges can be selected out of 4 is 4C2


Hence





Represent P(X),X in tabular form and calculating XP(X) and X2P(X) for mean and variance



Now mean is given by




E(X) = 0.4


Now variance is V(X) = E(X2) – [E(X)]2


E(X2) is given by




Hence




Cancel out 5




Hence mean is 0.4 and variance is


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