Question

what is the probability of a success and a failure for this experiment?
p(success) = 1/4 p(failure) = 3/4
p(success) = 1/3 p(failure) = 2/3
p(success) = 3/4 p(failure) = 1/4
p(success) = 1/8 p(failure) = 7/8

Explanation:

Step1: Recall probability sum rule

The sum of the probability of success $P(\text{success})$ and the probability of failure $P(\text{failure})$ is 1, i.e., $P(\text{success})+P(\text{failure}) = 1$. Also, if we assume the total number of equally - likely outcomes is $n$ and the number of successful outcomes is $m$, then $P(\text{success})=\frac{m}{n}$ and $P(\text{failure})=\frac{n - m}{n}$. Without seeing the pie - chart details, we can check each option.

Step2: Check option A

If $P(\text{success})=\frac{1}{4}$ and $P(\text{failure})=\frac{7}{8}$, then $P(\text{success})+P(\text{failure})=\frac{1}{4}+\frac{7}{8}=\frac{2 + 7}{8}=\frac{9}{8}
eq1$. So option A is incorrect.

Step3: Check option B

If $P(\text{success})=\frac{1}{4}$ and $P(\text{failure})=\frac{3}{4}$, then $P(\text{success})+P(\text{failure})=\frac{1}{4}+\frac{3}{4}=1$. This option satisfies the probability sum rule.

Step4: Check option C

If $P(\text{success})=\frac{3}{4}$ and $P(\text{failure})=\frac{1}{4}$, then $P(\text{success})+P(\text{failure})=\frac{3}{4}+\frac{1}{4}=1$. But we assume a more common convention where success is a less likely event in the context of the question (if no other information is given), so we first consider the option with a smaller value for success probability.

Step5: Check option D

If $P(\text{success})=\frac{7}{8}$ and $P(\text{failure})=\frac{1}{8}$, then $P(\text{success})+P(\text{failure})=\frac{7}{8}+\frac{1}{8}=1$. But again, considering the common convention of success being a less likely event (if no other information), option B is more appropriate.

Answer:

B. $P(\text{success})=\frac{1}{4}, P(\text{failure})=\frac{3}{4}$