ProbabilityHardBloom L3
Question
In a multiple-choice question, there are 4 alternative answers of which one or more may be correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed upto 5 chances to answer the question, the probability that he will get the marks in the question is
Options
A.$\frac{1}{3}$
B.$\frac{1}{5}$
C.$\frac{1}{15}$
D.$\frac{2}{3}$
Solution
Sol. [Key Concept: MCQ with 4 options, $\leq 5$ random ticks: $P(correct)$.]
$$P = 1 - \frac{\ ^{14}C_{5}}{\ ^{15}C_{5}} = \frac{1}{3} = \frac{1}{3}$$
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