Answer to Question #5958 in Statistics and Probability for mar
2012-01-12T08:23:39-05:00
find the probability distribution for the number of fails that occur when 4 coins are tossed?
1
2012-01-13T12:18:39-0500
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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