Question

Sonali can solve 70% of the problems in a competitive exam and Nirali can solve only 60% of the problems in the same exam. What is the probability that at least one of them will solve a problem, if the question is picked randomly from the same exam?

• A. 0.82
• B. 0.88
• C. 0.62
• D. 0.72

Hint:

Use 1 minus the probability that neither of them solves the problem.

Answer 1

The Correct Option is B

Step 1: Break "at least one" into three separate non overlapping cases.
The event "at least one solves it" is the sum of: only Sonali solves it, only Nirali solves it, and both solve it.

Step 2: Compute each case.
Only Sonali: $0.7 \times (1-0.6) = 0.7 \times 0.4 = 0.28$. Only Nirali: $(1-0.7) \times 0.6 = 0.3 \times 0.6 = 0.18$. Both solve it: $0.7 \times 0.6 = 0.42$.

Step 3: Add the three cases.
$0.28 + 0.18 + 0.42 = 0.88$.

Step 4: Cross check with the standard formula.
The formula $P(A \cup B) = P(A) + P(B) - P(A)P(B) = 0.7 + 0.6 - 0.42 = 0.88$ gives the same value, confirming the answer.

Final Answer:
The probability is 0.88. \[ \boxed{0.88} \]