Question

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.

Answer 1

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

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