Math Problem Statement

Let A be the event of rolling a die and getting​ 6, and let B be the event of tossing a coin and getting heads. When finding the probability that events A and B both​ occur, which formula​ applies? Question content area bottom Part 1 Choose the correct answer below. A.Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper B right parenthesis Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper B right parenthesis B.Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper B vertical line Upper A right parenthesis Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis plus Upper P left parenthesis Upper B vertical line Upper A right parenthesis C.Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis ·P left parenthesis Upper B vertical line Upper A right parenthesis Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis ·P left parenthesis Upper B vertical line Upper A right parenthesis D.Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis ·P left parenthesis Upper B right parenthesis Upper P left parenthesis Upper A and Upper B right parenthesis equals Upper P left parenthesis Upper A right parenthesis ·P left parenthesis Upper B right parenthesis

Solution

The correct formula to use for finding the probability that both events AA and BB occur (rolling a 6 on a die and getting heads on a coin flip) is:

D. P(A and B)=P(A)⋅P(B)P(A \text{ and } B) = P(A) \cdot P(B)

This is because the events are independent: the outcome of rolling a die does not affect the outcome of tossing a coin, and vice versa. For independent events, the probability of both occurring is the product of their individual probabilities.

So, P(A)P(A) is the probability of rolling a 6 on a die, which is 16\frac{1}{6}, and P(B)P(B) is the probability of getting heads on a coin flip, which is 12\frac{1}{2}. Therefore:

P(A and B)=16⋅12=112P(A \text{ and } B) = \frac{1}{6} \cdot \frac{1}{2} = \frac{1}{12}

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the probability of rolling a 5 and getting tails on a coin flip?
  2. How does the formula change if the events AA and BB are dependent?
  3. What is the probability of rolling an odd number and getting heads?
  4. If you flip two coins and roll a die, what is the probability of getting two heads and a 6?
  5. How would you find the probability of rolling a 6 twice and flipping heads?

Tip: For independent events, always multiply their probabilities to find the probability of both occurring.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

P(A and B) = P(A) · P(B) for independent events

Theorems

Multiplication rule for independent events

Suitable Grade Level

Grades 9-12

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