Probability
Probability
star_batch_jee_advanced_2025
Grade 12
Question:
A student appears for test I, II and III. The student is successful if he passes either in test I, II or I, III. The probability of the student passing in test I, II and III are respectively $p$, $q$ and $1/2$. If the probability of the student to be successful is $1/2$ then :
p = q = 1
p = q = 1/2
p = 1, q = 0
p = 1, q = 1/2
Step-by-Step Solution
Key Concept: Apply the general inclusion-exclusion formula for three sets and solve the resulting equation.
Expanding $P(I \cup I \cup III) = P(I) + P(II) - P(I \cap II) - P(I \cap III) - P(II \cap III) + P(I \cap II \cap III)$ gives $pq + \frac{p}{2} - \frac{pq}{2} - \frac{p}{2}(q+1) + \frac{1}{2} = 1$, which simplifies to $p(q+1) = 1$.
Correct Answer: 3