Question

In a multiple choice question, there are four alternative answers, of which one or more are correct. A candidate decides to tick the answers at random. If he is allowed u to 3 choices to answer the question, the probability that he will get arks in the question is

(a)1/15
(b)621/3375
(c)1/5
(d)4/15

Answer 1

To find the probability of getting at least three correct answers out of four alternatives, we calculate the probabilities of getting 3, 4, or 5 correct answers and add them up. The probability is 55/1024, or approximately 0.0537. Therefore, the correct answer is (a)1/15.

Step-by-step explanation:

To find the probability of getting at least three correct answers out of four alternatives, we will calculate the probability of getting 3, 4, or 5 correct answers and add them up.

The probability of a correct answer is 1/4 and the probability of an incorrect answer is 3/4.

Therefore, the probability of getting 3 correct answers out of 3 attempts is (1/4) * (1/4) * (1/4) * (3/4) * (3/4) * (3/4) = 27/256.

Similarly, the probability of getting 4 correct answers out of 3 attempts is (1/4) * (1/4) * (1/4) * (1/4) * (3/4) * (3/4) = 27/1024.

The probability of getting 5 correct answers out of 3 attempts is (1/4) ^ 5 = 1/1024.

Adding up these probabilities, we get (27/256) + (27/1024) + (1/1024) = 55/1024. Therefore, the probability of getting at least three correct answers is 55/1024, which is approximately 0.0537.