Question

A die is rolled thrice.what is the probability of sum of roll at least 5

Answer 1

Die is rolled thrice = 6 * 6 * 6

                               = 216.

The number of possible outcomes with Sum of at least 5 is : 

1 + 1 + 1 

1 + 1 + 2

2 + 1 + 1

1 + 2 + 1

There are 4 possibilities.

So, the probability with sum at least 5 is 1 - 4/216

                                                                  = 212/216

                                                                  = 53/54.


Hope this helps!

Answer 2

Answer:

212/216

Step-by-step explanation:

Let us assume the dice to be fair, each outcome on a single throw having a probability of 1/6.

Now sum of the rolls at least 5 => all outcomes other than with sum less than equal to 4.

Therefore reqd probability = 1-probability of getting sum<=4

So, let us see in how many ways can we get sum 4 in 3 rolls of the dice. The ordered possibilities are 1,2,1 ; 2,1,1 ; 1,1,2; that is only 3 possibilities.

Also, we can get sum 3 in 1 way , i.e. 1,1,1

Now, probability of each of these happening is 1/6 * 1/6 *1/6 = 1/216, assuming dice throws are independent.

So probability of getting sum of less than equal to 4= 4/216

Now it's complement would give us the answer , that is probability of getting at least 5 as the sum= 1–4/216= 212/216