A fair die is rolled 3 times. A 4 is considered "success", while all other outcomes are "failures". What is the probability of 2 successes?
1 Answer
Mar 1, 2017
# P("2 successes") = 5/72#
Explanation:
For any particular throe of the dice, then:
# P(S) = 1/6 ; P(F) = 5/6 #
So if we roll the dies three times; then the permutations are as follows;
Thus the probably of 2 successes is:
# P("2 successes") = P(FSS) + P(SFS) + (SSF) #
# " " = 5/6 1/6 1/6 + 1/6 5/6 1/6 + 1/6 1/6 5/6 #
# " " = 3* 5/6 1/6 1/6 #
# " " = 15/216 #
# " " = 5/72 #
