**Problem Statement:**A die is thrown twice. What is the probability that a 3 will result the first time and a 5 the second time? (Assume the die is six-sided with each side numbered one through six. Enter your probabilities as a fraction.)**Answer Box:** [Text box for entering the probability fraction]**Explanation:**When a six-sided die is thrown, each number (1 through 6) has an equal chance of appearing. Therefore, for any single roll, the probability of rolling a specific number, such as 3, is $ \frac{1}{6} $.The same logic applies to rolling a 5 on the second throw. Both events are independent, meaning the outcome of the first roll does not affect the second.To find the probability of two independent events both occurring, you multiply their probabilities:\[ P(\text{rolling a 3 first and a 5 second}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]So, the probability is $\frac{1}{36}$.

Name: **Problem Statement:**A die is thrown twice. What is the probability
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Description: **Problem Statement:**A die is thrown twice. What is the probability that a 3 will result the first time and a 5 the second time? (Assume the die is six-sided with each side numbered one through six. Enter your probabilities as a fraction.)**Answer

Given that a die is thrown twice. The number of possible outcomes when a die is thrown is 6 and the corresponding sample space is 1,2,3,4,5,6. When the die is thrown twice, the number of possible outcomes is 62=36. The sample space when a die is thrown twice is as follows. 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, 6,6We have to find the probability that a 3 will result the first time and a 5 in the second time. From the above sample space, we can see that the only favourable outcome is 3,5. So, the the probability that a 3 will result the first time and a 5 in the second time = number of favourable outcomestotal number of outcomes=136.

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Advanced Math

A die is thrown twice. What is the probability that a 3 will result the first time and a 5 the second time? (Assume the die is six sided with each side numbered one through six. Enter your probabilities as a fraction.)

A die is thrown twice. What is the probability that a 3 will result the first time and a 5 the second time? (Assume the die is six sided with each side numbered one through six. Enter your probabilities as a fraction.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Topic Video

Question

**Problem Statement:**

A die is thrown twice. What is the probability that a 3 will result the first time and a 5 the second time? (Assume the die is six-sided with each side numbered one through six. Enter your probabilities as a fraction.)

**Answer Box:** [Text box for entering the probability fraction]

**Explanation:**

When a six-sided die is thrown, each number (1 through 6) has an equal chance of appearing. Therefore, for any single roll, the probability of rolling a specific number, such as 3, is $ \frac{1}{6} $.

The same logic applies to rolling a 5 on the second throw. Both events are independent, meaning the outcome of the first roll does not affect the second.

To find the probability of two independent events both occurring, you multiply their probabilities:

\[ P(\text{rolling a 3 first and a 5 second}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36} \]

So, the probability is $\frac{1}{36}$.

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