If you flip one coin and roll one six-sided number cube, find the probability of landing on tails and rolling an even number at the same time. Write your answer as a simplified fraction.(1 point)

Answer 1

To find the probability of landing on tails when flipping a coin and rolling an even number on a six-sided die, we can break it down into two parts:

1. Probability of landing on tails (coin flip): A standard coin has two sides: heads and tails. The probability of getting tails is: \[ P(\text{Tails}) = \frac{1}{2} \]

2. Probability of rolling an even number (six-sided die): A six-sided die has the numbers 1, 2, 3, 4, 5, and 6. The even numbers on the die are 2, 4, and 6. Thus, there are 3 favorable outcomes (even numbers) out of 6 total outcomes. The probability of rolling an even number is: \[ P(\text{Even number}) = \frac{3}{6} = \frac{1}{2} \]

3. Combined Probability: Since the coin flip and the die roll are independent events, we can find the combined probability by multiplying the probabilities of each individual event: \[ P(\text{Tails and Even number}) = P(\text{Tails}) \times P(\text{Even number}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]

Thus, the probability of landing on tails and rolling an even number at the same time is: \[ \boxed{\frac{1}{4}} \]