Question 854302
if you randomly pick one of the boxes and then one of the fruits in the box, what is the probability that a red apple from the blue box will be picked.


if you randomly pick a box then 1/2 of the time you will get a blue box and 1/2 of the time you will get a red box.


the blue box contains 3 apples and 1 banana in it for a total of 4 pieces of fruit.


since the probability of one of the apples in the blue box being green is 1/3, this means you must have 1 green apple and 2 red apples in the blue box.


the probability of randomly picking a fruit from the blue box and having that piece of fruit being a red apple is equal to 2/3 * 3/4 = 2/4 which is equal to 1/2.


probability of 2/3 is because you have 3 apples and 2 of them are red.
probability of 3/4 is because you have 3 apples out of a total of 4 fruits.


this stands to reason since out of 4 fruits in the blue box, 2 of them are red apples so the probability is 2/4 that you will get a red apple out of the blue box and 2/4 is equivalent to 1/2.


since you only pick the blue box half of the time, the probability is therefore equal to 1/2 * 1/2  = 1/4.