Question

a examination consists of 8 questions in each of which one of 5 alternative is the correct one. on the assumption that a candidate who has done no preparatory work chooses for each question any one of the five alternative with equal probability , the probability that he gets more than one correct ans is equal to?

Answer 1

a examination consists of 8 questions in each of which one of 5 alternative is the correct one. On the assumption that a candidate who has done no preparatory work chooses for each question any one of the five alternative with equal probability, the probability that he gets more than one correct ans is equal to?

There are 3 possibilities:

1) he gets no correct answers

2) he gets one correct answer

3) he gets more than one correct answer

Therefore:

$$P(> 1) + P(1) + P(0) = 1$$

probability that he gets more than one correct answer equals:

$$P(> 1) = 1 - P(1) - P(0)$$

$P(1)$ - probability that he gets one correct answer

$P(0)$ - probability that he gets no correct answers

$$P(0) = \left(\frac{4}{5}\right)^8$$

$\frac{4}{5}$ - probability that he gets wrong answer for 1 question, 8 - number of questions

$$P(1) = 8 \left(\frac{4}{5}\right)^7 \frac{1}{5}$$

$\frac{1}{5}$ - probability that he gets correct answer for 1 question, 7 - number of "wrong" questions, 8 - number of possibilities to get 1 correct answer (8 questions)

$$P(> 1) = 1 - 8 \left(\frac{4}{5}\right)^7 \frac{1}{5} - \left(\frac{4}{5}\right)^8 = \frac{194017}{390625} \approx 0.5$$

Answer: $P(> 1) = \frac{194017}{390625} \approx 0.5$