Question

1. A biology test consists of 5 true or false questions. A student who sat for the examination tried to answer each question by nearly guessing without reading each statement. The probability of the student scoring exactly 4 correct is?

Answer 1

A biology test consists of 5 true or false questions. A student who sat for the examination tried to answer each question by nearly guessing without reading each statement. The probability of the student scoring exactly 4 correct is?

Probability that he answered correctly (or wrong) on the question $= \frac{1}{2}$ (There are only 2 possibilities for answer—True or False).

Probability that he would get 4 correct answers $= \left(\frac{1}{2}\right)^{4}$

Probability that he would get 1 wrong answer $= \left(\frac{1}{2}\right)^{1}$

Therefore, probability that he would get 4 correct answers and 1 wrong in certain order $= \left(\frac{1}{2}\right)^{5}$.

There are 5 possibilities to get wrong answer (on first question, second … )

Therefore, probability that he would get 4 correct answers equals:

$$P = 5 * \left(\frac{1}{2}\right)^{5} = \frac{5}{32}$$

Answer: $\frac{5}{32}$