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How well do you understand the concepts and skills introduced in this lesson?

Which is the formula to calculate the probability that at least one of a set of independent events occurs?

  1. \( P\left( B \middle| A \right) \cdot P\left( A \right) = P(A \text{ and } B) \)
  2. \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)} \)
  3. \( P\left( A \text{ and } B \right) = P(A) \cdot P(B) \)

This is the formula to calculate the probability that at least one of a set of independent events occurs.

This is a different way to state the conditional probability formula.

This is a conditional probability formula.

Use this formula to find the probability that both independent events occur.

What is the probability of rolling an even number on a fair twenty-sided die given that you first rolled an odd number on a fair six-sided die?

  1. \( 0.25 \)
  2. \( 0.08 \)
  3. 0.667

Use the formula \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \) Let event B = "rolling an even on a 20-sided die" and let event A = "rolling an odd on a 6-sided die."

Use the formula \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \) Let event B = "rolling an even on a 20-sided die" and let event A = "rolling an odd on a 6-sided die."

Use the formula \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \) Let event B = "rolling an even on a 20-sided die" and let event A = "rolling an odd on a 6-sided die."

Use the formula \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \) Let event B = "rolling an even on a 20-sided die" and let event A = "rolling an odd on a 6-sided die."

The probability that a person has brown eyes is 79%. The probability that a person lives in a house is 56%. What is the probability that a randomly selected person has brown eyes and lives in a house?

  1. 70.9%
  2. 90.8%
  3. 135%

These two events are independent. Use the formula \( P\left( A \text{ and } B \right) = P(A) \cdot P(B) \).

These two events are independent. Use the formula \( P\left( A \text{ and } B \right) = P(A) \cdot P(B) \).

These two events are independent. Use the formula \( P\left( A \text{ and } B \right) = P(A) \cdot P(B) \).

These two events are independent. Use the formula \( P\left( A \text{ and } B \right) = P(A) \cdot P(B) \).

Which is the BEST definition of an independent event?

  1. An event whose probabilities are affected by the outcomes of other events.
  2. An event whose probability can be calculated using the conditional probability formula.
  3. An event whose probability is always equal to 1.

This is a description of a dependent event.

The outcomes of independent events have no effect on the other events.

The conditional probability formula can be used only with dependent events.

The probability of an independent event may or may not be equal to 1.

Which events are dependent?

  1. You toss a coin that lands on heads and then roll a die, which lands on 3.
  2. You randomly pick a pair of blue socks from your drawer, return them, and then select a pair of green socks.
  3. The school choir had an extra rehearsal, so you wear a coat to school.

A coin toss is independent from a die roll.

Since you replaced the first pair of socks, these events are independent.

These events are dependent.

These two events are not related.

The two-way frequency table below shows the enrollment of freshmen and sophomore students in music and art classes at a certain school.
Music Class Art Class Total
Freshman 136 58 194
Sophomore 64 42 106
Total 200 100 300

Find the probability that a randomly selected student is enrolled in a music class given that they are a sophomore.

  1. 32%
  2. 35.3%
  3. 66.7%

Use the two-way table to calculate the conditional probability. You can also use the conditional probability formula, \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \)

Use the two-way table to calculate the conditional probability. You can also use the conditional probability formula, \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \)

Use the two-way table to calculate the conditional probability. You can also use the conditional probability formula, \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \)

Use the two-way table to calculate the conditional probability. You can also use the conditional probability formula, \( P\left( B \middle| A \right) = \frac{P \ (A \text{ and } B)}{P \ (A)}. \)

Summary

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