Question

A single die is rolled twice. the 36​ equally-likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 5.

Answer 1

Total possible outcome = 36

Outcome with sums is 5 = 4
{1, 4} (2, 3} {3, 2} {4, 1} 

P(getting sum = 5) = 4/36 = 1/9

Answer: 1/9

Answer 2

Given: A single die is rolled twice.

To Find: Probability of getting two numbers whose sum is 5.

Solution: The required probability is \frac{1}{9}[/tex]

Explanation:

When we roll a die once, there are 6 possible outcomes.

When we roll the same die once again, there will be a total of 6*6=36 possible outcomes.

This is the set of total possible outcomes

${{ (1,1), (1,2), (1,3), (1,4),(1,5), (1,6),\\(2,1), (2,2), ... , (2,6)\\(3,1),(3,2),...,(3,6)\\(4,1),(4,2)...(4.6)\\(5,1),(5,2),...(5,6)\\(6,1),(6,2),...,(6,6)}}$

Now let us see the number of outcomes of getting two numbers whose sum is 5. This is possible when a 1 and 4 are rolled (1,4) and (4,1) or when a 2 and 3 are rolled (2,3) and (3,2).

Thus, there are 4 possible outcomes for this.

Therefore the probability will be $\frac{4}{36}= \frac{1}{9}$