So if 2 people get to roll 2 dices on their next turn what is the probability of one of them hitting a 6

To find the probability of at least one person rolling a sum of 6 with two dice, we need to calculate the probability of each person not rolling a 6 and then find the complement.

First, let's determine the probability of rolling a sum of 6 with two dice.

The possible outcomes when rolling two dice are:

\[
(1,5), (2,4), (3,3), (4,2), (5,1)
\]

There are 5 outcomes that result in a sum of 6. The total number of possible outcomes when rolling two dice is:

\[
6 \times 6 = 36
\]

So, the probability of rolling a sum of 6 with two dice is:

\[
\frac{5}{36}
\]

Now, let's find the probability of not rolling a sum of 6:

\[
1 - \frac{5}{36} = \frac{31}{36}
\]

Since we are dealing with two independent events (two people rolling the dice), the probability that both do not roll a sum of 6 is:

\[
\left(\frac{31}{36}\right) \times \left(\frac{31}{36}\right) = \left(\frac{31}{36}\right)^2 = \frac{961}{1296}
\]

The probability that at least one person rolls a sum of 6 is the complement of both not rolling a sum of 6:

\[
1 - \frac{961}{1296} = \frac{335}{1296}
\]

So, the probability that at least one person rolls a sum of 6 is:

\[
\frac{335}{1296} \approx 0.258
\]

Therefore, the probability of at least one person rolling a sum of 6 on their turn is approximately 0.258 or 25.8%.

Would you like more details on any part of this calculation or have any other questions?

Here are 5 questions you might consider asking:

1. How do you calculate the probability of rolling a specific sum with two dice?
2. What are the odds of rolling doubles with two dice?
3. Can you explain how to calculate the probability of multiple independent events?
4. What is the probability of rolling a sum of 7 with two dice?
5. How do you calculate the expected value of a dice roll?

**Tip:** When calculating probabilities of multiple events, always consider whether the events are independent or dependent, as this affects the overall probability calculation.

Understand how to calculate the probability of at least one person rolling a sum of 6 with two dice. Detailed solution covering probability concepts, including the complement rule and independent events. Suitable for Grades 10-12 students.

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