A box contains 2 red and 3 blue balls. Two balls are drawn successively. If getting 'a red ball on first draw and a blue ball on second draw' is considered a success, then write the probability distribution of successes. It is given that the above experiment is performed 3-times, with replacement

Explanation

Let R stands for Red balls and B for Blue balls

`Success : Red on first draw and blue on second draw`
`P(success)= P =((2R)/(5B))*((3B)/(4R))=3/10`
`P(failure)=q=1-3/10=7/10`
`P(X=0)+P(X=1)+P(X=2)+P(X=3)`
`3C_0p^0q^3+3C_1p^1q^2+3C_2p^2q^1+3C_0p^3q^0`
`=1*1*(7/10)^3 + 3*(3/10)^1*(7/10)^2+3*(3/10)^2(7/10)+(3/10)^3`
`=343/1000+(9*49)/1000+(27*7)/1000+27/1000`

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