Question

what is the probability of a success and a failure for this experiment? \\( \bigcirc \\ p(\text{success}) = \frac{1}{4}; \\ p(\text{failure}) = \frac{7}{8} \\) \\( \bigcirc \\ p(\text{success}) = \frac{1}{4}; \\ p(\text{failure}) = \frac{3}{4} \\) (selected) \\( \bigcirc \\ p(\text{success}) = \frac{3}{4}; \\ p(\text{failure}) = \frac{1}{4} \\) \\( \bigcirc \\ p(\text{success}) = \frac{7}{8}; \\ p(\text{failure}) = \frac{1}{8} \\)

Explanation:

Step1: Analyze the pie chart

The pie chart is divided into 8 equal - like parts (visually, we can assume equal sectors for probability calculation). Let's assume the success region and failure region.

Step2: Calculate total parts

The total number of parts \(n = 8\)? Wait, no, let's check the options. Wait, maybe the success has 2 parts? Wait, no, let's look at the probability values. The sum of probability of success and failure should be 1. Let's check each option:

• Option 1: \(\frac{1}{4}+\frac{7}{8}=\frac{2 + 7}{8}=\frac{9}{8}

eq1\), so wrong.

• Option 2: \(\frac{1}{4}+\frac{3}{4}=\frac{1 + 3}{4}=1\), this satisfies the condition that \(P(\text{success})+P(\text{failure}) = 1\) (since in a probability experiment, the sum of probability of an event and its complement is 1).
• Option 3: \(\frac{3}{4}+\frac{1}{4}=1\), but let's check the pie chart. Wait, the pie chart has numbers 4,5,6,7 and some other sectors. Wait, maybe the success is 2 sectors (since \(\frac{2}{8}=\frac{1}{4}\)) and failure is 6 sectors (\(\frac{6}{8}=\frac{3}{4}\)). So the probability of success is \(\frac{1}{4}\) and failure is \(\frac{3}{4}\) as their sum is 1.
• Option 4: \(\frac{7}{8}+\frac{1}{8}=1\), but if we check the pie chart, the numbers 4,5,6,7 are in some sectors, and the other sectors (maybe 1,2,3) are less. But from the sum of probabilities, option 2 has \(P(\text{success})=\frac{1}{4}\) and \(P(\text{failure})=\frac{3}{4}\) which sums to 1, and the other options either don't sum to 1 (option 1) or the proportion doesn't match the visual (option 4: 7/8 success is too much, option 3 reverses success and failure).

Answer:

B. \(P(\text{success})=\frac{1}{4}; P(\text{failure})=\frac{3}{4}\) (assuming the option with the blue dot is the second option, and we re - label the options as A, B, C, D: A. \(P(\text{success})=\frac{1}{4}; P(\text{failure})=\frac{7}{8}\), B. \(P(\text{success})=\frac{1}{4}; P(\text{failure})=\frac{3}{4}\), C. \(P(\text{success})=\frac{3}{4}; P(\text{failure})=\frac{1}{4}\), D. \(P(\text{success})=\frac{7}{8}; P(\text{failure})=\frac{1}{8}\)) So the correct answer is B. \(P(\text{success})=\frac{1}{4}; P(\text{failure})=\frac{3}{4}\)