Question

stat 213 assignment 1: problem 4 (1 point) a quick quiz consists of 5 multiple - choice problems, each of which has 4 answers, only one of which is correct. if you make random guesses on all 5 problems. (a) what is the probability that all 5 of your answers are incorrect? (use four decimals) answer (b) what is the probability that all 5 of your answers are correct? (use four decimals) answer note: you can earn partial credit on this problem.

Explanation:

Step1: Find probability of getting one answer wrong

Each question has 4 answers with 1 correct and 3 incorrect. So the probability of getting one answer wrong is $\frac{3}{4}= 0.75$.

Step2: Calculate probability of all 5 answers wrong

Since the guesses for each question are independent events, we use the multiplication - rule for independent events. The probability that all 5 answers are wrong is $(0.75)^5$.
$(0.75)^5=0.2373$

Step3: Find probability of getting one answer right

The probability of getting one answer right is $\frac{1}{4} = 0.25$.

Step4: Calculate probability of all 5 answers right

Using the multiplication - rule for independent events, the probability that all 5 answers are right is $(0.25)^5$.
$(0.25)^5=0.0009765625\approx0.0010$

Answer:

(a) 0.2373
(b) 0.0010