Question

Two urns both contain green balls and red balls. Urn I contains 6 green balls and 4 red balls and Urn II contains 8 green balls and 7 red balls. A ball is drawn from each urn. What is the probability that both balls are red?

Answer 1

Presumably, whatever is drawn from Urn I is independent of what is drawn from Urn II. This means

$P(\text{red from Urn 1 AND red from Urn 2})=P(\text{red from Urn 1})\cdot P(\text{red from Urn 2})$

We have

$P(\text{red from Urn 1})=\dfrac4{10}=\dfrac25$

$P(\text{red from Urn 1})=\dfrac7{15}$

so the probability of drawing red balls from both urns is $\dfrac25\cdot\dfrac7{15}=\dfrac{14}{75}$