5 white b***s and k black b***s are placed into a bin. Two of the b***s are drawn at random. The probability that one of the drawn b***s is white and the

We have

P(White ball is drrawn first) +  P (black ball is drawn first)  = 10/21

5/ [5 + k]  * [ k]/ [ 4+k]  +  [ k]/[5 + k] * [ 5]/ [4 + k]  = 10/21

[5k  + 5k]  / [ (5 + k) (4 + k)] = 10/21

[10k] / [ k^2 + 9k + 20 ]  = 10/21

k / [ k^2 + 9k + 20 ]  =1/21     cross−multiply

[ k^2 + 9k + 20 ]  = 21k

k^2 − 12k + 20   = 0    factor

(k − 10) (k − 2)  = 0       set each factor to  0 and  k =2  or  k=10

So ..... k = 2

Proof :   5/ [7]  * [ 2]/ [ 6]  +  [ 2]/[7] * [ 5]/ [6]   = 10/42  + 10/42  = 20/42  = 10/21