Question

1. using the venn diagram shown, find:

explain

probability = \\(\frac{6 + 7 + 13}{6 + 7 + 13 + 11}\\)

probability = \\(\frac{26}{37}\\)

3 points on the board!

6d \\(p(\text{neither } a \text{ nor } b)\\)

probability = enter your next step here

Explanation:

Step1: Identify the total number of elements

The total number of elements is the sum of all regions in the Venn diagram, which is \(6 + 7 + 13 + 11\). Calculating that: \(6+7 = 13\), \(13+13 = 26\), \(26 + 11 = 37\). So total \(n = 37\).

Step2: Identify the region for neither A nor B

The region that is neither in A nor in B is the part not in A or B. From the previous parts, the regions in A or B are \(6 + 7 + 13\), so the region neither A nor B is the remaining part, which is \(11\) (from the total regions: \(6,7,13\) are in A or B, and \(11\) is outside both).

Step3: Calculate the probability

Probability \(P(\text{neither } A \text{ nor } B)\) is the number of elements neither in A nor B divided by the total number of elements. So that's \(\frac{11}{37}\).

Answer:

\(\frac{11}{37}\)