A bag contains 2 white marbles , 4 blue marbels , and 6 red marbles . A marble is drawn at random from the bag . What is the probability that
it is blue ?

Options

A. `3`
B. `6`
C. `10`
D. `12`

Answer

A, B, C

Explanation

`(a,b,c)` Let the no. of blue marbles is `a` and no. of green marbles is `b` .
`:.(ab)/("^(a+b)C_(2))=(1)/(2)`
`implies(a+b)(a+b-1)=4ab`
`impliesb^(2)-(2a+1)b+a^(2)-a=0`
but `b in R implies D=(2a+1)^(2)-4(a^(2)-a)=8a+1`
`:. 8a+1` must be a perfect square.
Hence possible values of `a` are `3,6,10`