# 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 #