Q1. What is the probability that at least one of the weatherman's 320 forecasts is incorrect?

Background

Topic: Probability of Complementary Events

This question tests your understanding of the complement rule in probability, specifically for repeated independent events.

Key Terms and Formulas

• Complement Rule:

• Probability of no errors in 320 forecasts: , where is the probability of being wrong.

Step-by-Step Guidance

1. Identify the probability of being wrong for a single forecast: .

2. Calculate the probability of being correct for a single forecast: .

3. Find the probability that all 320 forecasts are correct: .

4. Apply the complement rule to find the probability that at least one forecast is incorrect: .

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Q2. If a student is selected at random, what is the probability the student wants to be Popular?

Background

Topic: Basic Probability from a Two-Way Table

This question tests your ability to calculate simple probabilities using frequency tables.

Key Terms and Formulas

• Probability:

Step-by-Step Guidance

1. Find the total number of students: Add all values in the table.

2. Find the number of students who want to be popular: Add the "Be Popular" values for boys and girls.

3. Set up the probability formula:

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Q3. What is the probability the student wants to be popular given it is a girl?

Background

Topic: Conditional Probability

This question tests your understanding of conditional probability using a two-way table.

Key Terms and Formulas

• Conditional Probability:

Step-by-Step Guidance

1. Find the total number of girls: Add all values in the "Girls" row.

2. Find the number of girls who want to be popular: Use the "Be Popular" value for girls.

3. Set up the conditional probability formula:

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Q4. What is the probability the student is a girl given we selected a student wanting to be popular?

Background

Topic: Conditional Probability (Reverse)

This question tests your ability to reverse the conditioning in probability using a two-way table.

Key Terms and Formulas

• Conditional Probability:

Step-by-Step Guidance

1. Find the total number of students who want to be popular: Add "Be Popular" values for boys and girls.

2. Find the number of girls who want to be popular: Use the "Be Popular" value for girls.

3. Set up the conditional probability formula:

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Q5. Are being Popular and being a Girl independent?

Background

Topic: Independence of Events

This question tests your understanding of independence in probability, using conditional and marginal probabilities.

Key Terms and Formulas

• Events are independent if

Step-by-Step Guidance

1. Recall the probability a student wants to be popular:

2. Recall the probability a student wants to be popular given they are a girl:

3. Compare these two probabilities. If they are equal, the events are independent; if not, they are dependent.

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