Question

1. find the probability of answering the two multiple choice questions correctly if random guesses are made. assume the questions each have five choices for the answer. only one of the choices is correct. a) 0.02 b) 0.4 c) 0.004 d) 0.04

Explanation:

Step1: Calculate the probability of answering one question correctly

The probability of answering one multiple - choice question correctly with 5 choices (only one correct) is \(P(\text{one correct})=\frac{1}{5}= 0.2\)

Step2: Use the multiplication rule for independent events

Since the two questions are independent events (the outcome of the first question does not affect the outcome of the second question), the probability of answering both questions correctly is \(P(\text{both correct})=P(\text{first correct})\times P(\text{second correct})\)

Substitute \(P(\text{first correct}) = P(\text{second correct})=0.2\) into the formula: \(P(\text{both correct})=0.2\times0.2\)

\(P(\text{both correct}) = 0.04\)

Answer:

D. 0.04