Suppose I have two boxes. They look identical to me. However, I am told: “Box A contains 1 red ball and three white balls; Box B has 2 red balls and 2 white balls.”
I randomly pick a box and select a ball from the box without looking into the box.
It is a red ball. What is the probability that I have picked Box A? Choose one of the following options.
A. Less than 30%. B. 30% ~ 50% (30 % is included; 50% is not included). C 50%. D. 50% ~ 60% (50% is not included; 60% is included). E. More than 60%.
P(Picking Red ball)$=(1+2)/(1+3+2+2)=3/8$
P(Picking Red Ball From Box A)$=1/2*1/4=1/8$
We want P(Picking Box A|Red Ball Picked)=P(Picking a Red ball from Box A)\P(Red Ball Picked)
Therefore, probability is $=(1/8)/(3/8)=1/3$ Answer is A.
Am I doing this correctly? My tutor is known for giving not-so straightforward questions, so I'm wondering if I need to consider another way, or I could be wrong. Any alternatives welcome too!