Each of three balls are randomly placed into one of three bowls. Find the probability distribution for Y = the number of empty bowls.
-
3-0-0: 3!/2! = 3 ways
2-1-0: 3! = 6 ways
1-1-1 3!/3 = 1 way
total ways = 10
Y P[Y]
0 1/10
1 6/10
2 3/10
--------
2-1-0: 3! = 6 ways
1-1-1 3!/3 = 1 way
total ways = 10
Y P[Y]
0 1/10
1 6/10
2 3/10
--------