A question in mathematics is given to three students P, Q and R whose chances…
2021
A question in mathematics is given to three students P, Q and R whose chances of solving are 1/3, 1/4, 1/5 respectively. What is the probability that the problem will be solved?
- A.
0.4
- B.
0.6
- C.
0.8
- D.
0.7
Attempted by 25 students.
Show answer & explanation
Correct answer: B
Step-by-Step Solution
Given:
Probability that P solves the problem = 1/3
Probability that Q solves the problem = 1/4
Probability that R solves the problem = 1/5
We need to find the probability that the problem is solved, i.e., at least one student solves it.
Step 1: Find the probability that each student fails
P fails = 1 − 1/3 = 2/3
Q fails = 1 − 1/4 = 3/4
R fails = 1 − 1/5 = 4/5
Step 2: Find the probability that none of them solves the problem
Assuming their attempts are independent,
Probability (none solve)
= (2/3) × (3/4) × (4/5)
= 2/5
= 0.4
Step 3: Find the probability that at least one solves the problem
Probability (at least one solves)
= 1 − Probability (none solve)
= 1 − 2/5
= 3/5
= 0.6
Final Answer: 0.6