1. There are two boxes: A and B; and 48 balls: 12 red, 12 blue, and 24 green. (a

Question

1. There are two boxes: A and B; and 48 balls: 12 red, 12 blue, and 24 green.

(a) If every ball is randomly thrown into one of the two boxes, what is the total number of ways

for the balls to be distributed in the two boxes?

(b) If every ball is individually labeled by numbers to make them distinguishable, should be expect

the number of ways of ball distributions to go up or down? Provide your answer and reasoning.

(c) Considering one instance where 2 red balls, 2 blue balls, and 4 green balls are in box A If one

of the boxes is selected at random and one ball is drawn, what is the probability to draw a red

ball from box A?

Explanation / Answer

(a) If every ball is randomly thrown into one of the two boxes, what is the total number of ways

for the balls to be distributed in the two boxes?

Ans: total no. of ways, 12 red balls can be distributed into 2 boxes = 12+1=13

total no. of ways, 12 blues balls can be distributed into 2 boxes = 12+1=13

total no. of ways, 24 red balls can be distributed into 2 boxes = 24+1= 25

thus, total no. of ways all the balls can be distributed into 2 boxes = 13*13*25 = 4225

(b) If labels are assigned, then the number of ways for arrangement will go up since all the ball will turn distinguishable i.e.in 2 red balls there will be many combinations of 2 balls being chosen from 12 red balls which will be =12*11 & so on

(c) This conditional prob & Bayes theorem application

P(ball=red | box=A) = 2/8=1/4

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