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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!