(a) Four chips are to be randomly put into four boxes, find the probability that exactly one box is empty. Assume that the chips are identical, and the boxes are labeled 1,2,3 and 4 respectively.

(b)Four chips are to be randomly put into four boxes, find the probability that exactly one box is empty. Assume that the chips are of different color, say red, green, blue and yellow, and the boxes are labeled 1,2,3,and 4, respectively.

Question

(a) Four chips are to be randomly put into four boxes, find the probability that exactly one box is empty.  Assume that the chips are identical, and the boxes are labeled 1,2,3 and 4 respectively.

(b)Four chips are to be randomly put into four boxes, find the probability that exactly one box is empty. Assume that the chips are of different color, say red, green, blue and yellow, and the boxes are labeled 1,2,3,and 4, respectively.

anonymous · Answer

@mathmate

onepieceftw · Answer

There are 4 boxes and 4 chips, so if you randomly put chips in the boxes then the probability is 1:4

anonymous · Answer

There are 4 boxes and 4 chips, so if you randomly put chips in the boxes then the probability is 1:4

kropot72 · Answer

(a) The probability of the first chip missing being put randomly into any one of the four boxes is given by:
P(first chip misses) = 1 - 1/4 = 3/4
The probability that the second chip misses the same box is also 3/4. The probabilities that the third and fourth chip also miss the same box are both 3/4.
Therefore the probability that the same box is empty after all four chips are placed is given by:
$$\large P(a\ box\ is\ empty\ after\ 4\ chips\ placed)=(\frac{3}{4})^{4}=you\ can\ calculate$$

anonymous · Answer

I'm just now getting back to this question....thank you so much @kropot72!!

kropot72 · Answer

You're welcome :)