Can anyone show me how to do these?

In the game of Yahtzee, suppose you have dice 1-2-4-5-6. What is the probability of rolling the 1 and 2 once and getting a large straight?

What is the porbability of rolling the 1 and 2 twice and getting a large straight?

To calculate the probability of these scenarios in Yahtzee, we need to understand the concept of probability and the rules of the game.

First, let's define a few terms:
- A large straight in Yahtzee is a sequence of five consecutive numbers, such as 1-2-3-4-5 or 2-3-4-5-6.
- In each turn of Yahtzee, you roll five dice.

Now, let's calculate the probability for each scenario you mentioned:

1. Probability of rolling the 1 and 2 once and getting a large straight:
To get a large straight, we need to roll either 1-2-3-4-5 or 2-3-4-5-6.

There are two ways to achieve this:
a) Roll the sequence 1-2-3-4-5.
b) Roll the sequence 2-3-4-5-6.

The probability of rolling each individual number on a fair six-sided die is 1/6. Since we are rolling 5 dice independently in each turn, the probability of getting both 1 and 2 in a single turn is (1/6) * (1/6) = 1/36.

The total probability of getting a large straight in one turn when we have 1 and 2 is 2 * (1/36) = 2/36 = 1/18.

2. Probability of rolling the 1 and 2 twice and getting a large straight:
In this scenario, we have two turns to get the desired large straight.

In the first turn: The probability of getting a large straight is 1/18. In this case, we have already accounted for the scenario of rolling a large straight in one turn.

In the second turn: We still need to roll the remaining dice and hope to get the missing numbers to form a large straight. As there are three remaining dice after the first turn, the probability of getting the required numbers is (1/18) * (1/6) * (1/6) * (1/6) = 1/3888.

The total probability of rolling the 1 and 2 twice and getting a large straight is 1/18 * 1/3888 = 1/69984.

So, the probability for the first scenario is 1/18, while the probability for the second scenario is 1/69984.