To Win The Game, Elena Has To Roll An Even Number First And A Number Less Than 3 Second. Her Probability Of Winning Is $\frac{6}{36}$.Marta Has A Lower Probability Of Winning Than Elena Has. Which Could Be The Outcome That Marta Needs To Win

Understanding the Problem

To win the game, Elena has to roll an even number first and a number less than 3 second. Her probability of winning is $\frac{6}{36}$. This means that out of 36 possible outcomes, Elena has a $\frac{6}{36}$ chance of winning. But what about Marta? We are told that Marta has a lower probability of winning than Elena has. So, what could be the outcome that Marta needs to win?

Analyzing the Possible Outcomes

Let's break down the possible outcomes for Elena and Marta. For Elena to win, she needs to roll an even number first and a number less than 3 second. This means that the possible outcomes for Elena are:

• 2 (even number) and 1 (number less than 3)
• 2 (even number) and 2 (number less than 3)
• 4 (even number) and 1 (number less than 3)
• 4 (even number) and 2 (number less than 3)
• 6 (even number) and 1 (number less than 3)
• 6 (even number) and 2 (number less than 3)

There are 6 possible outcomes for Elena to win. But what about Marta? We are told that Marta has a lower probability of winning than Elena has. This means that Marta's probability of winning is less than $\frac{6}{36}$.

Finding the Outcome for Marta

To find the outcome that Marta needs to win, we need to find the outcome that has a lower probability of winning than Elena's. Let's analyze the possible outcomes for Marta:

• 1 (odd number) and 1 (number less than 3)
• 1 (odd number) and 2 (number less than 3)
• 3 (odd number) and 1 (number less than 3)
• 3 (odd number) and 2 (number less than 3)
• 5 (odd number) and 1 (number less than 3)
• 5 (odd number) and 2 (number less than 3)

We can see that the outcome 1 (odd number) and 1 (number less than 3) has a lower probability of winning than Elena's. This is because there are only 18 possible outcomes where the first roll is 1, and only 6 of those outcomes have the second roll as 1. Therefore, the probability of Marta winning is $\frac{6}{18} = \frac{1}{3}$, which is less than Elena's probability of winning.

Conclusion

In conclusion, the outcome that Marta needs to win is rolling an odd number first and a number less than 3 second. This outcome has a lower probability of winning than Elena's, and it is the only outcome that meets this condition.

Calculating the Probability

To calculate the probability of Marta winning, we need to count the number of possible outcomes where the first roll is an odd number and the second roll is a number less than 3. There are 18 possible outcomes where the first roll is 1, and 6 of those outcomes have the second roll as 1. There are 6 possible outcomes where the first roll is 3, and 2 of those outcomes have the second roll as 1. There are 6 possible outcomes where the first roll is 5, and 2 of those outcomes have the second roll as 1. Therefore, the total number of possible outcomes where Marta wins is 18 + 6 + 6 = 30. The probability of Marta winning is therefore $\frac{30}{36} = \frac{5}{6}$.

Comparing the Probabilities

To compare the probabilities of Elena and Marta winning, we need to calculate the probability of each outcome. We have already calculated the probability of Marta winning as $\frac{5}{6}$. To calculate the probability of Elena winning, we need to count the number of possible outcomes where Elena wins. There are 6 possible outcomes where Elena wins, and the probability of each outcome is $\frac{1}{6}$. Therefore, the probability of Elena winning is $\frac{6}{36} = \frac{1}{6}$.

Conclusion

In conclusion, the outcome that Marta needs to win is rolling an odd number first and a number less than 3 second. This outcome has a lower probability of winning than Elena's, and it is the only outcome that meets this condition. The probability of Marta winning is $\frac{5}{6}$, while the probability of Elena winning is $\frac{1}{6}$.

Final Answer

The final answer is that the outcome that Marta needs to win is rolling an odd number first and a number less than 3 second.

Understanding the Problem

To win the game, Elena has to roll an even number first and a number less than 3 second. Her probability of winning is $\frac{6}{36}$. This means that out of 36 possible outcomes, Elena has a $\frac{6}{36}$ chance of winning. But what about Marta? We are told that Marta has a lower probability of winning than Elena has. So, what could be the outcome that Marta needs to win?

Analyzing the Possible Outcomes

Let's break down the possible outcomes for Elena and Marta. For Elena to win, she needs to roll an even number first and a number less than 3 second. This means that the possible outcomes for Elena are:

• 2 (even number) and 1 (number less than 3)
• 2 (even number) and 2 (number less than 3)
• 4 (even number) and 1 (number less than 3)
• 4 (even number) and 2 (number less than 3)
• 6 (even number) and 1 (number less than 3)
• 6 (even number) and 2 (number less than 3)

There are 6 possible outcomes for Elena to win. But what about Marta? We are told that Marta has a lower probability of winning than Elena has. This means that Marta's probability of winning is less than $\frac{6}{36}$.

Finding the Outcome for Marta

To find the outcome that Marta needs to win, we need to find the outcome that has a lower probability of winning than Elena's. Let's analyze the possible outcomes for Marta:

• 1 (odd number) and 1 (number less than 3)
• 1 (odd number) and 2 (number less than 3)
• 3 (odd number) and 1 (number less than 3)
• 3 (odd number) and 2 (number less than 3)
• 5 (odd number) and 1 (number less than 3)
• 5 (odd number) and 2 (number less than 3)

We can see that the outcome 1 (odd number) and 1 (number less than 3) has a lower probability of winning than Elena's. This is because there are only 18 possible outcomes where the first roll is 1, and only 6 of those outcomes have the second roll as 1. Therefore, the probability of Marta winning is $\frac{6}{18} = \frac{1}{3}$, which is less than Elena's probability of winning.

Q&A

Q: What is the probability of Elena winning?

A: The probability of Elena winning is $\frac{6}{36} = \frac{1}{6}$.

Q: What is the probability of Marta winning?

A: The probability of Marta winning is $\frac{5}{6}$.

Q: What is the outcome that Marta needs to win?

A: The outcome that Marta needs to win is rolling an odd number first and a number less than 3 second.

Q: Why does Marta have a lower probability of winning than Elena?

A: Marta has a lower probability of winning than Elena because the outcome that Marta needs to win has fewer possible outcomes than the outcome that Elena needs to win.

Q: How many possible outcomes are there for Elena to win?

A: There are 6 possible outcomes for Elena to win.

Q: How many possible outcomes are there for Marta to win?

A: There are 30 possible outcomes for Marta to win.

Q: What is the probability of each outcome for Elena?

A: The probability of each outcome for Elena is $\frac{1}{6}$.

Q: What is the probability of each outcome for Marta?

A: The probability of each outcome for Marta is $\frac{5}{6}$.

Conclusion

In conclusion, the outcome that Marta needs to win is rolling an odd number first and a number less than 3 second. This outcome has a lower probability of winning than Elena's, and it is the only outcome that meets this condition. The probability of Marta winning is $\frac{5}{6}$, while the probability of Elena winning is $\frac{1}{6}$.