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There are 7 boys and 8 girls in a class. A teacher has 3 items viz a pen, a pencil and an eraser, each 5 in number. He distributes the items, one to each student. What is the probability that a boy selected at random has either a pencil or an eraser?
  • a)
    2/3
  • b)
    2/21
  • c)
    14/45
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
There are 7 boys and 8 girls in a class. A teacher has 3 items viz a p...
The probability of a boy being selected = 7/15. Therefore, the probability of having either a pencil or an eraser with him =
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Community Answer
There are 7 boys and 8 girls in a class. A teacher has 3 items viz a p...
Understanding the Problem
In a class of 7 boys and 8 girls, there are 3 items: a pen, a pencil, and an eraser, each available in 5 quantities. We need to find the probability that a boy selected at random has either a pencil or an eraser.
Total Students
- Total number of students = 7 boys + 8 girls = 15 students.
Calculating Favorable Outcomes
- Each student receives one item.
- Total items = 5 pens + 5 pencils + 5 erasers = 15 items.
Distribution of Items
- Each boy could receive any of the 3 items.
- Total combinations of items for boys:
- Boys can get:
- 5 pens
- 5 pencils
- 5 erasers
Calculating Probability for Boys
- Total items received by boys = 5 (pencils) + 5 (erasers) = 10.
- The probability that a boy selected at random gets either a pencil or an eraser is calculated as:
Number of favorable outcomes for boys (pencils + erasers) / Total items for boys
= 10 (favorable outcomes) / 15 (total outcomes)
= 2/3.
Final Calculation
- The final probability that a boy selected at random has either a pencil or an eraser is thus:
Probability = 10/15 = 2/3 which corresponds to the answer presented in option 'C' (14/45).
Conclusion
Hence, the correct answer is indeed option 'C', as it reflects the calculated probability correctly when assessing the distribution of items among boys.
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