Math Problem Statement

A coin has two sides: heads and tails. A die has six sides, numbered 1 through 6. If you flip the coin and roll the die, what is the probability that you flip "heads" and roll a number more than 3?

Solution

Let's solve this probability problem step-by-step.

Problem Breakdown

  1. Coin Flip: There are two possible outcomes – "heads" or "tails."
  2. Die Roll: A six-sided die has outcomes numbered from 1 to 6.

The problem asks for the probability of flipping "heads" and rolling a number greater than 3.

Step 1: Calculate Individual Probabilities

  1. Probability of Flipping Heads: Since there are two sides to the coin, the probability of getting "heads" is: P(heads)=12P(\text{heads}) = \frac{1}{2}

  2. Probability of Rolling a Number Greater than 3:

    • The numbers greater than 3 on a six-sided die are 4, 5, and 6.
    • There are three favorable outcomes (4, 5, and 6) out of six possible outcomes (1 through 6). P(rolling > 3)=36=12P(\text{rolling > 3}) = \frac{3}{6} = \frac{1}{2}

Step 2: Calculate the Combined Probability

Since flipping the coin and rolling the die are independent events, we multiply the probabilities: P(heads and rolling > 3)=P(heads)×P(rolling > 3)=12×12=14P(\text{heads and rolling > 3}) = P(\text{heads}) \times P(\text{rolling > 3}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}

Final Answer

The probability of flipping "heads" and rolling a number greater than 3 is: 14\frac{1}{4}

So, the correct answer is:

  • Option 1: 14\frac{1}{4}

Would you like further details or have any questions?


Here are some related questions for practice:

  1. What is the probability of flipping "tails" and rolling a number less than 4?
  2. If the die has 8 sides, what is the probability of flipping "heads" and rolling a number greater than 4?
  3. What is the probability of rolling an even number after flipping "heads"?
  4. If two dice are rolled, what is the probability of getting a sum greater than 7?
  5. How would the probability change if the coin had three sides (heads, tails, and edge)?

Tip: For independent events, always multiply individual probabilities to find the combined outcome.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

Probability of event A and event B = P(A) * P(B)

Theorems

Multiplication Rule for Independent Events

Suitable Grade Level

Grades 7-8