Mathematics Middle School

if you rolled two dice what is the probability that you would roll a sum of 10

Answers

Answer 1

The probability of rolling a sum of 10 with two dice is 1/12.

What is probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.

Given that two dice are rolled and find the probability of a sum of 10.

The sample space of the event of rolling two dice is

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

      (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

      (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

      (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

      (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

      (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

The total possible outcomes is 36.

The favorable outcomes that is the outcomes where the sum is 10 is

(1, 4), (2, 3), (3, 2).

The number of favorable outcomes are 3.

To find the probability of rolling a sum of 10 with two dice, write the sample space and then determine the number of favorable outcomes that is the outcomes where the sum is 10 and the total number of possible outcomes.

The formula to find out the probability of any event is:

[tex]\text{P(event)} = \dfrac{(\text{number of favorable outcomes})}{\text{total number of possible outcomes}}[/tex]

By using the data and formula, the probability of rolling a sum of 10 is,

[tex]\text{P(event)} = \dfrac{(\text{number of favorable outcomes})}{\text{total number of possible outcomes}}[/tex]

[tex]\text{P(rolling a sum of 10)} = \dfrac{3}{36}[/tex]

On dividing both numerator and denominator by 3 gives,

[tex]\text{P(rolling a sum of 10)} = \dfrac{1}{12}[/tex]

Hence, the required probability of rolling a sum of 10 with two dice is 1/12.

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Answer 2

The probability that you would roll a sum of 10 if you rolled two dice is 1/12.

We need to consider all the possible outcomes and count the favorable outcomes to determine the probability of rolling a sum of 10 when rolling two dice.

When rolling two dice, each die has six possible outcomes, ranging from 1 to 6. To find the total number of outcomes, we multiply the number of outcomes for each die: 6 * 6 = 36.

Next, we need to count the number of favorable outcomes, which are the combinations of two dice that result in a sum of 10. These combinations include:

1. Rolling a 4 on the first die and a 6 on the second die: (4, 6)

2. Rolling a 5 on the first die and a 5 on the second die: (5, 5)

3. Rolling a 6 on the first die and a 4 on the second die: (6, 4)

There are three favorable outcomes.

Therefore, the probability of rolling a sum of 10 when rolling two dice is:

Probability = (Number of favorable outcomes) / (Number of total outcomes) = 3/36 = 1/12.

Hence, the probability is 1/12.

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