Questions: Similarly, what is the probability that the sum of the dots on the rolling of two dice is greater than or equal to 8? That is find P(x ≥ 8)? Do not simplify your fraction. Use the table below to help. x 2 3 4 5 6 7 8 9 10 11 12 p(x) 1/36 2/36 3/36 4/36 5/36 6/36 5/36 4/36 3/36 2/36 1/36

Solution Steps

To find the probability that the sum of the dots on the rolling of two dice is greater than or equal to 8, we need to sum the probabilities of all outcomes where the sum is 8 or more. According to the given table, these outcomes are 8, 9, 10, 11, and 12. We will add the probabilities for these outcomes to find the desired probability.

To find the probability that the sum of the dots on the rolling of two dice is greater than or equal to 8, we need to consider the probabilities of the sums 8, 9, 10, 11, and 12. From the given data, these probabilities are:

• \( P(8) = \frac{5}{36} \)
• \( P(9) = \frac{4}{36} \)
• \( P(10) = \frac{3}{36} \)
• \( P(11) = \frac{2}{36} \)
• \( P(12) = \frac{1}{36} \)

The probability of the sum being greater than or equal to 8 is the sum of the probabilities of these individual outcomes: \[ P(x \geq 8) = P(8) + P(9) + P(10) + P(11) + P(12) \] \[ P(x \geq 8) = \frac{5}{36} + \frac{4}{36} + \frac{3}{36} + \frac{2}{36} + \frac{1}{36} \]

Adding these probabilities gives: \[ P(x \geq 8) = \frac{5 + 4 + 3 + 2 + 1}{36} = \frac{15}{36} \]

Final Answer