Twelve balls are distribute among three boxes. The probability that the first box contains three balls is a.`(110)/9(2/3)^(10)` b. `(9)/110(2/3)^(10)` c. `((12)C_3)/(12^3)xx2^9` d. `((12)C_3)/(3^(12))`

Options

A. `55/3((2)/(3))^(11)`
B. `55((2)/(3))^(10)`
C. `220((1)/(3))^(12)`
D. `22((1)/(3))^(11)`

Answer

A

Explanation

Since the 3 boxes are identical, probability of selecting a box (in which we are to put 3 balls) is 1/3.
`impliesp=1/3,q=1-1/3=2/3`
Probability that the selected box should contain exactly 3 balls is the same as probability of exactly 3 success in 12 trails (putting the 12 balls in 3 boxes).
`therefore"Required probability"=""^(12)C_(3)((1)/(3))^(3)((2)/(3))^(9)=55/2((2)/(3))^(11)`