SOLUTION: A blue box has 3 apples and 1 banana in it, and a red box has 5 apples and 6 bananas in it. The apples in the blue box have the probability 1/3 of being green and 2/3 of being red

Algebra ->  Probability-and-statistics -> SOLUTION: A blue box has 3 apples and 1 banana in it, and a red box has 5 apples and 6 bananas in it. The apples in the blue box have the probability 1/3 of being green and 2/3 of being red      Log On


   

Question 854302: A blue box has 3 apples and 1 banana in it, and a red box has 5 apples and 6 bananas in it. The apples in the blue box have the probability 1/3 of being green and 2/3 of being red. The apples in the red box have the probability of 1/4 of being green and 3/4 of being red. If we randomly pick one of the boxes and then one of the fruits in that boxes.
What is the probability that a red apple from the blue box is selected
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Blue box: 4 fruit: 1GA, 2RA, Banana

P(pick red apple from red box  0r pick from blue box) = %28%282%2F3%293%29%2F4+%2B+%28%283%2F4%295%29%2F11+=+1%2F2+%2B+15%2F44

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.