# Combinations and probability distributions

Question:
Three balls are thrown at random into 5 bowls so that each ball has the same chance of going into any bowl independently of wherever the other 2 balls fall. Determine the probability distribution of the numberof empty bowls.

The anwers are below, but i don't understand them. Can it be looked at as a success failure type poblem. with probability of success being that a bowl gets 1 ball: probability = 1/5, and the probability of a failure; 1-1/5 = 4/5. If so how do I use this to obtain the distribution.

Also can someone please tell me why in this scenario we don't look at the possibility of the ball missing the bowl - because i feel that this should be a possibility in this scenario, which then gives 6 equally likely outcomes, which would mean probabitlity of a success is then 1/6?

The anwer to this question (which I don't understand) is:
if we let R = no. of empty bowls

the distribution of R:
P(R=2) = 0.48, p(R=3) = 0.48, p(R=4) = 0.04

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tiny-tim
Homework Helper
Hi SavvyAA3! Can it be looked at as a success failure type poblem. with probability of success being that a bowl gets 1 ball: probability = 1/5, and the probability of a failure; 1-1/5 = 4/5.
Yes, that's right! If so how do I use this to obtain the distribution.

P(R=2) = 0.48, p(R=3) = 0.48, p(R=4) = 0.04
Well, try p(R=4) first … that's the probability that the second and third balls go into the same bowl as the first one … which is … ? Also can someone please tell me why in this scenario we don't look at the possibility of the ball missing the bowl - because i feel that this should be a possibility in this scenario, which then gives 6 equally likely outcomes, which would mean probabitlity of a success is then 1/6?
erm … REALITY CHECK … ! When you're sitting in the examination room, THE ONLY REALITY IS WHAT'S ON THE QUESTION PAPER … anything else is just a mirage brought about by heat and lack of water and sleep. why reality check? The question did not state that this is not a possibility - please tell me why I can't assume this?

Thanks.

The question also didn't state that aliens would not grab the balls with a tractor beam or that your dog would not eat them... do you see?

tiny-tim
Homework Helper
Hi montoyas7940! The question also didn't state that aliens would not grab the balls with a tractor beam
hmm … … is that what happened to you … ? Hi yourself TT!

No, fortunately aliens didn't grab my balls. 