What is the probability that a sum of 5 on the 2 dice will occur at least once?

Question

Use the formula for the probability of the complement of an event.

A pair of dice is rolled 3 times. What is the probability that a sum of 5 on the 2 dice will occur at least once? (Round your answer to three decimal places.)

Answer 1

The question says that you roll the pair of dice three times, and you want the probability that you get a sum of 5 at least once.

Let X = the sum of the 2 dice.

P(X=5) = 4/36 = 1/9 (4 ways to get 5, 36=6² different results of 2 dice )

P(X≠5) = 1 - 1/9 = 8/9

P(at least one 5) = 1 - P(No 5's) (see the latest video I posted here for explanation of why this is so)

For three rolls:

P(at least one 5) = 1 - [P(X≠5)]³ = 1 - (8/9)³ ≈ .2977

Answer 2

sum of 5 happens either as 4+1,1+4, 3+2 or 2+3, a total of 4 ways

total outcomes are 6x6=36

P(exactly 5 on two dice) = 4/36 = 1/9 = 11.111...% = about 11% chance