Question

Nikki is flipping a coin and rolling two dice what is the probability the result of a coin flip is heads and the result of rolling the two dice sums to 11 show all your work

Answer 1

First, let's determine the total number of outcomes for flipping a coin and rolling two dice.

For the coin flip, there are 2 possible outcomes (heads or tails).

For rolling two dice, the total number of outcomes is 6 * 6 = 36, as there are 6 possible outcomes for each dice.

Therefore, the total number of outcomes for flipping a coin and rolling two dice is 2 * 36 = 72.

Now, let's determine the number of favorable outcomes for the result of a coin flip being heads and the result of rolling the two dice summing to 11.

For the coin flip to be heads, there is 1 favorable outcome.
For the dice to sum to 11, the possible outcomes are:
(5, 6), (6, 5)

So there are 2 favorable outcomes for the dice summing to 11.

Therefore, the number of favorable outcomes for the desired result is 1 * 2 = 2.

The probability of the result of a coin flip being heads and the result of rolling the two dice summing to 11 is:
Number of favorable outcomes / Total number of outcomes
= 2 / 72
= 1 / 36

So the probability is 1/36 or approximately 0.0278.