In a multiple choice question, there are four alternative answers, of which one or more are correct. A candidate will get marks only if they tick all the correct answers.
If the candidate chooses answers at random and is allowed up to three chances to answer the question, find the probability that they will get marks in the question.
Step-by-step Solution:
Each option can either be selected or not selected (2 choices), so for 4 options, total number of non-empty subsets (possible answer combinations) is:
\(
2^4 - 1 = 15
\)
(We subtract 1 for the null set, which corresponds to choosing nothing.)
So, total number of possible distinct answer combinations = 15
Since the candidate is allowed up to 3 guesses, they can choose 3 different combinations.
Out of these 15 combinations, only one is correct (the exact correct subset of options).
So, the number of favorable outcomes = 3 (if the correct one is among the 3 chosen)
Probability of getting marks:
\(
\text{Probability} = \frac{3}{15} = \frac{1}{5}
\)