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?
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?
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Use 1 minus the probability that neither of them solves the problem.
Updated On: Jul 30, 2026
- 0.82
- 0.88
- 0.62
- 0.72
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The Correct Option is B
Approach Solution - 1
To find the probability that at least one of Sonali or Nirali will solve a problem, we can use the concept of complementary probability. The steps involved are as follows:
- Calculate the probability that Sonali does not solve the problem:
- The probability that Sonali can solve a problem is 70%, which is 0.70 in decimal form.
- Thus, the probability that she does not solve a problem is \(1 - 0.70 = 0.30\).
- Calculate the probability that Nirali does not solve the problem:
- The probability that Nirali can solve a problem is 60%, which is 0.60 in decimal form.
- Therefore, the probability that she does not solve a problem is \(1 - 0.60 = 0.40\).
- Calculate the probability that neither Sonali nor Nirali solves the problem. Since their abilities to solve the problem are independent events, use the rule of multiplication for independent events:
- Probability that neither solves the problem is \(0.30 \times 0.40 = 0.12\).
- Find the probability that at least one of them solves the problem by subtracting the probability that neither solves the problem from 1:
- \(1 - 0.12 = 0.88\)
Therefore, the probability that at least one of Sonali or Nirali will solve the problem is 0.88.
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Approach Solution -2
Step 1: Write down the individual solving chances.
Sonali solves a random problem with probability 0.7, so she fails to solve it with probability \(1 - 0.7 = 0.3\). Nirali solves it with probability 0.6, so she fails with probability \(1 - 0.6 = 0.4\).
Step 2: Find the probability that neither solves it.
Since the two events are independent, the chance both fail is \(0.3 \times 0.4 = 0.12\).
Step 3: Use the complement rule for "at least one".
"At least one solves it" is everything except "neither solves it", so its probability is \(1 - 0.12 = 0.88\).
Final Answer:
The probability that at least one of them solves the problem is 0.88. \[ \boxed{0.88} \]
Sonali solves a random problem with probability 0.7, so she fails to solve it with probability \(1 - 0.7 = 0.3\). Nirali solves it with probability 0.6, so she fails with probability \(1 - 0.6 = 0.4\).
Step 2: Find the probability that neither solves it.
Since the two events are independent, the chance both fail is \(0.3 \times 0.4 = 0.12\).
Step 3: Use the complement rule for "at least one".
"At least one solves it" is everything except "neither solves it", so its probability is \(1 - 0.12 = 0.88\).
Final Answer:
The probability that at least one of them solves the problem is 0.88. \[ \boxed{0.88} \]
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