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Answer to Question #5958 in Statistics and Probability for mar

Question #5958
find the probability distribution for the number of fails that occur when 4 coins are tossed?
Expert's answer
Let n be the number of fails.

Here are all possible results:

0 fails:
0 0 0 0
(1 possibility)

1 fail:
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
(4 possibilities)

2 fails:
1 1 0 0
1 0 1 0
1 0 0 1
0 1 1 0
0 1 0 1
0 0 1 1
(6 possibilities)

3 fails:
0 1 1 1
1 0 1 1
1 1 0 1
1 1 1 0
(4 possibilities)

4 fails:
1 1 1 1
(1 possibility)

Wee see that there are 1+4+6+4+1 = 16 possible rusults. So,

P(n=0) = 1/16,
P(n=1) = 4/16 = 1/4,
P(n=2) = 6/16 = 3/8,
P(n=3) = 1/4,
P(n=4) = 1/16.

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