Question

question 7 points 1

find the probability of getting heads on flipping a coin and then rolling an odd number on a single 6-sided die.

1/4
1/3

Explanation:

Identify the individual events

We need to find the probability of two consecutive events occurring:

1. Flipping a coin and getting heads.
2. Rolling a single 6-sided die and getting an odd number.

Calculate the probability of the first event

Using the Independent Events knowledge point:
The probability of flipping a coin and getting heads, denoted as \(P(\text{Heads})\), is:

$$ P(\text{Heads}) = \frac{1}{2} $$

Calculate the probability of the second event

Using the Independent Events knowledge point:
A standard 6-sided die has outcomes \(\{1, 2, 3, 4, 5, 6\}\). The odd numbers are \(\{1, 3, 5\}\).
The probability of rolling an odd number, denoted as \(P(\text{Odd})\), is:

$$ P(\text{Odd}) = \frac{3}{6} = \frac{1}{2} $$

Calculate the compound probability

Using the Independent Events knowledge point:
Since the outcome of the coin flip does not affect the outcome of the die roll, these are independent events. We multiply their individual probabilities:

$$ P(\text{Heads and Odd}) = P(\text{Heads}) \times P(\text{Odd}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $$

Answer:

• (A) 1/4 (Correct answer)
• (B) 1/3