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.
Best Answer
These are two independent events so you just need to find the probability of each and then multiply.
Probability that the ball from first bag is white=$4/6$
Probability that the ball from second bag is white=$3/8$
So the answer is $4/6\times3/8=1/4.$
What you have found is the probability that pick a white ball in this experiment: We first pick a bag at random that then pick a ball at random.