When a pair of dice are rolled there are 36 different possible outcomes: 1-1, 1-2, ... 6-6. If a pair of dice are rolled 3 times, what is the probability of getting a sum of 5 every time? Round to eight decimal places.

The probability of getting a sum of 5 every time is 0,137174%

Step-by-step explanation:

First we have to get the probability of getting a 5 when we rolled 2 dices.

1+1=2 / / 1+2=3 / / 1+3=4 / / 1+4=5 the rest are higher

2+1=3 / / 2+2=4 / / 2+3=5 the rest are higher

3+1=4 / / 3+2=5 the rest are higher

4+1=5 the rest are higher

The rest of the sum are higher.

So, the P (getting a sum of 5) = 4/36=0.11

When two or more events are independent, the probability of all occurring is the product of the probabilities of the individual events. More formally, if events A and B are independent, then the probability of both A and B and C occurring is:

P (A and B and C) = P (A) x P (B) x P (B)

In this case,

P (A and B and C) = 4/36 x 4/36 x4/36

P (A and B and C) = 0.00137174