A bag contains $4$ white balls and $2$ black balls , another contains $3$ white balls and $5$ black balls . If one ball is drawn from each bag, determine the probability that both are white .
$ a.)\ \dfrac13 \\ b.)\ \dfrac23 \\ \color{green}{ c.)\ \dfrac14 } \\ d.)\ \dfrac34 $
I did $\dfrac12 \times \dfrac46 + \dfrac12 \times \dfrac38=\dfrac{25}{48} $
But the answer is given as option $c.)$
I look for a short and simple way .
I have studied maths upto $12$th grade.