Question

When two six-sided dice are rolled, there are 36 possible outcomes. a. Find the probability that the sum is not 4. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. b. Find the probability that the sum is greater than 5. Express your first answer as a fraction in simplest form, and round your percent answer to the nearest whole percent. Round the fraction

Answer 1

Answer:

Step-by-step explanation:

First let's calculate the probability of the sum of the cubes being 4, so we can subtract it from 100% to get the probability of the sum not being 4.

In order to be 4 we have the following outcomes.

Outcomes = {(1, 3), (2, 2)}, there are 2 outcomes out of 36 when the sum is equal to 4.

P(Sn4) = $100 \% - \frac{2}{36} \cdot 100 \% = 100 \% - \frac{100 \%}{18} = 100 \% (1 - \frac{1}{18}) = 100 \% \cdot \frac{17}{18} \approx 94 \%$

Now to find the probability of the sum being greater than 5, we'll find the probability of it being less than or equal to 5.

Outcomes = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 3)}, there are 6 outcomes out of 36.

Now to find the probability of the sum of the dice being greater than 5, we'll subtract the probability of the sum being less than or equal to 5 from 100%.

P(Bgt5) = $100 \% - [\frac{6}{36} \cdot 100 \%] = 100 \% (1 - \frac{1}{6}) = 100 \% \cdot \frac{5}{6} \approx 83 \%$