Q21 of 26 Page 1

Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution.

Given: There are five bad oranges and 20 good oranges


To find: the probability distribution of number of bad oranges drawn and mean and variance of the distribution


Let X denote the number of bad oranges drawn in four oranges from 5 bad oranges and 20 good oranges


X can be five value i.e. 0, 1, 2, 3, 4 as there are 5 bad oranges


Now,


Probability of getting 0 bad oranges = P(X=0)









Probability of getting 1 bad orange = P(X=1)








Probability of getting 2 bad oranges = P(X=2)







Probability of getting 3 bad oranges = P(X=3)







Probability of getting 4 bad oranges = P(X=4)











Formula used:




Therefore,





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