Combinations and probability distributions

[SavvyAA3]

Can someone please help with the method of how to solve this problem...

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

Please help!

 

[tiny-tim]

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.

 

[SavvyAA3]

why reality check? The question did not state that this is not a possibility - please tell me why I can't assume this?

Thanks.

 

[montoyas7940]

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]

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 … ? ​

 

[montoyas7940]

Hi yourself TT!

No, fortunately aliens didn't grab my balls.

But I read about this guy once...