Jacqueline is taking a quiz in her science class. Each problem has only 1 correct answer. Problem 1 has answer choices A through D and Problem 2 is a true-or-faise problem. What is the probability that Jacqueline will select the correct answer for problems 1 and 27
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![### Compound Probability in Mathematics
#### Lesson 16: Mastery Assessment
**Problem 11: Jacqueline's Science Quiz**
Jacqueline is taking a quiz in her science class. Each problem has only one correct answer.
1. **Problem 1** has answer choices A through D.
2. **Problem 2** is a true-or-false problem.
**Question:**
What is the probability that Jacqueline will select the correct answer for both Problems 1 and 2?
**Answer Choices:**
- \( \frac{1}{2} \)
- \( \frac{1}{8} \)
- \( \frac{1}{3} \)
- \( \frac{1}{4} \)
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### Explanation of Graphs or Diagrams
In this question, no graphs or diagrams are provided. The problem tests understanding of basic probability concepts where:
- The probability of guessing correctly on Problem 1 (with 4 choices) is \( \frac{1}{4} \).
- The probability of guessing correctly on Problem 2 (true-or-false) is \( \frac{1}{2} \).
To find the combined probability of both events happening (correct answers for both problems), you multiply the individual probabilities:
\[
P(\text{Correct on Problem 1 and Problem 2}) = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}
\]
Therefore, the correct answer is \( \frac{1}{8} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa518261f-56eb-4fb2-a5d5-3ea220a98396%2F87677fc2-26bf-424a-bb3f-e1294a6df2d7%2F9aejjo_processed.jpeg&w=3840&q=75)
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