Question

1. using the venn diagram shown, find:

explain
probability = \\(\frac{6 + 5 + 12}{6 + 5 + 12 + 8}\\)
probability = \\(\frac{23}{31}\\)
3 points on the board!
4d \\(p(\text{neither } a \text{ nor } b)\\)
probability = enter your next step here

Explanation:

Step1: Identify the region for neither A nor B

The region for neither \( A \) nor \( B \) is the part not in \( A \) and not in \( B \). From the total elements \( 6 + 5 + 12 + 8 \), the element not in \( A \) or \( B \) is \( 8 \).

Step2: Calculate the probability

The probability \( P(\text{neither } A \text{ nor } B) \) is the number of elements in neither \( A \) nor \( B \) divided by the total number of elements. So, \( \text{Probability} = \frac{8}{6 + 5 + 12 + 8} \)

Step3: Simplify the fraction

First, calculate the denominator: \( 6 + 5 + 12 + 8 = 31 \). So the probability is \( \frac{8}{31} \)

Answer:

\(\frac{8}{31}\)