A game involves picking coloured balls from two boxes, referred to as
Box 1 and Box 2. Box 1 contains two red balls and seven green balls.
Box 2 contains four green balls and three red balls. The balls are
identical in every respect except for their colour. A blindfolded
player first chooses a box and then picks a ball. If a certain player
picks a red ball, what is the probability that the player chose from
Box 1?
The formula I have used to solve this is Bayes Theron
Plugging in the numbers asked in the question
= .2/ or 20%
Is this the correct answer also did I use the formula correctly?
Best Answer
$p(1\text{ and }R)=\frac{1}{2}\cdot\frac{2}{9}=\frac{1}{9}$. $p(2\text{ and }R)=\frac{1}{2}\cdot\frac{3}{7}=\frac{3}{14}$. Hence $$p(1|R)=\frac{\frac{1}{9}}{\frac{1}{9}+\frac{3}{14}}=\frac{14}{41}$$