**Puzzle:** You have 3 baskets and each basket contains exactly 4 balls, each balls is of the same size. Each ball is either red, black, yellow, or orange, and there is one of each color in each basket.

If you were blindfolded, and lightly shook each basket so that the balls would be randomly distributed, and then took 1 ball from each basket, what chance is there that you would have exactly 2 red balls?

**Solution:**

There are 64 different possible outcomes, and in 9 of these, exactly 2 of the balls will be red. There is thus a slightly better than 14% chance [(9/64)*100] that exactly 2 balls will be red.

A other way to solve the problem is to look at it this way.

There are 3 scenarios where exactly 3 balls are red:

1 2 3

———–

R R X

R X R

X R R

X is any ball that is not red.

There is a 4.6875% chance that each of these situations will occur.

Take the first one, for example: 25% chance the first ball is red, multiplied by a 25% chance the second ball is red, multiplied by a 75% chance the third ball is not red. Because there are 3 scenarios where this outcome occurs, you multiply the 4.6875% chance of any one occurring by 3, & you get 14.0625%

I think other way to explain this would be by Binomial distribution.

Here n= 3, r = 2 and theta = (1/4 = 0.25).

By putting this in equation, we will the answer.

ans = (theta)^r * (1-theta)^(n-r)

so the right answer is 14.0625. Ok?

Total Possible Outcomes: Box1(4 ways) x Box2(4 ways) x Box3(4 ways) = 64 total outcomes

Out of this 64 total outcomes there are 9 favourable outcomes where exactly 2 of the balls will be red.

R R X = 3 chances (R R B, R R Y, R R O)

R X R = 3 chances (R B R, R Y R, R O R)

X R R = 3 chances (B R R, Y R R, O R R)

Probablility =9/64 = 14.06 %

thanks saranya

@saranya u have given an explanation which is easily understandable….Thanks for your Reply with good explanation!!!!

Thanks saranya!! well explained.