Nikki is flipping a coin and rolling two dice. What is the probability that the result of a coin flip is heads and the result of rolling the two dice sums to 11. Show all your work.(2 points)

Question

Nikki is flipping a coin and rolling two dice. What is the probability that the result of a coin flip is heads and the result of rolling the two dice sums to 11. Show all your work.(2 points)

Answer 1

To find the probability of the result of a coin flip being heads and the sum of the two dice being 11, we need to find the individual probabilities of each event and then multiply them together.

1. Coin flip:
Since there are 2 possible outcomes (heads or tails) and they are equally likely, the probability of getting heads is 1/2.

2. Rolling two dice:
There are 36 possible outcomes when rolling two dice (6 possibilities for the first die and 6 possibilities for the second die). To determine the number of outcomes that sum to 11, we need to list them out:
(5,6), (6,5)
This gives us 2 successful outcomes out of 36 total outcomes.

Now, to find the probability of both events happening, we multiply the probabilities together:
P(coin flip = heads) * P(dice sum = 11) = 1/2 * 2/36 = 1/2 * 1/18 = 1/36

Therefore, the probability of the result of a coin flip being heads and the result of rolling the two dice summing to 11 is 1/36.

Answer 2

simplify into a paragraph

Answer 3

The probability of both flipping a coin and rolling two dice is calculated by first determining the individual probabilities of each event. The chance of getting heads on a coin flip is 1/2, as there are two possible outcomes (heads or tails) that are equally likely. When rolling two dice, there are 36 total outcomes, and only 2 of those outcomes result in a sum of 11 - specifically, rolling a 5 and a 6, or a 6 and a 5. By multiplying the probability of getting heads (1/2) with the probability of rolling a sum of 11 (2/36), we find that the overall probability of the result of a coin flip being heads and the sum of the two dice being 11 is 1/36.