Math Problem Statement

A coin is flipped and a die is rolled. What is the probability of getting heads and rolling a 5?

Solution

To find the probability of getting heads on the coin flip and rolling a 5 on the die, we can follow these steps:

  1. Coin Flip: The probability of getting heads when flipping a coin is: P(Heads)=12P(\text{Heads}) = \frac{1}{2}

  2. Die Roll: The probability of rolling a 5 on a six-sided die is: P(Rolling a 5)=16P(\text{Rolling a 5}) = \frac{1}{6}

Since the coin flip and die roll are independent events, the probability of both events happening together is the product of their individual probabilities: P(Heads and Rolling a 5)=P(Heads)×P(Rolling a 5)=12×16=112P(\text{Heads and Rolling a 5}) = P(\text{Heads}) \times P(\text{Rolling a 5}) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}

Thus, the probability of getting heads and rolling a 5 is 112\frac{1}{12}.

Do you want more details or have any questions?

Here are 5 related questions:

  1. What is the probability of getting tails and rolling a 3?
  2. What is the probability of flipping heads and rolling an even number?
  3. How many possible outcomes are there when flipping a coin and rolling a die?
  4. If you flip two coins and roll one die, what is the probability of getting two heads and rolling a 6?
  5. What is the probability of getting heads and rolling a number less than 4?

Tip: When dealing with independent events, the probability of both occurring is the product of their individual probabilities.

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Math Problem Analysis

Mathematical Concepts

Probability
Independent Events

Formulas

P(A and B) = P(A) * P(B)
P(Heads) = 1/2
P(Rolling a 5) = 1/6

Theorems

Multiplication Rule for Independent Events

Suitable Grade Level

Grades 6-8