Question

Consider a pop quiz with five questions- 4 true/false and one multiple choice. Each true/false question has two possible answers and the multiple choice question has four possible answers(a-d). Suppose a student takes the quiz without studying and randomly guesses on all five questions. What's the probability that the student answers at least ONE question correctly?

Answer 1

hint: at least one means "not none"

Answer 2

The probability of getting zero questions correct in the true/false group of 4 questions can be found by the binomial distribution as follows:
\[P(0\ true/false\ correct)=\left(\begin{matrix}4 \\ 0\end{matrix}\right)0.5^{0}\times 0.5^{4}=you\ can\ calculate\]
The probability of choosing an incorrect answer in the multiple choice question is 3/4.
The probability of getting zero questions correct is the product of the two above-mentioned probabilities.
When you have found P(zero questions correct) subtract from 1.0000 to find the probability of getting one or more questions correct.