In a class of 16 students (9 boys and 7 girls), the teacher randomly distributes 6 markers, 5 crayons, and 5 sketch pens, giving one item to each student such that each student receives exactly one item.

Consider the following statements:
Statement I: The probability that a randomly selected student is a boy who receives either a crayon or a sketch pen is 25/96.
Statement II: The probability that a randomly selected student is a girl who receives a marker is 21/128.
Select the correct answer from the options below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

Question

In a class of 16 students (9 boys and 7 girls), the teacher randomly distributes 6 markers, 5 crayons, and 5 sketch pens, giving one item to each student such that each student receives exactly one item.

Consider the following statements:
Statement I: The probability that a randomly selected student is a boy who receives either a crayon or a sketch pen is 25/96.
Statement II: The probability that a randomly selected student is a girl who receives a marker is 21/128.
Select the correct answer from the options below:
(a) Only Statement I is correct.
(b) Only Statement II is correct.
(c) Both Statements I and II are correct.
(d) None of the Statements is correct.

TutorArc · Accepted Answer

Total ways of assigning items = 1 item per student &rarr; uniform random distribution
Favourable outcomes for Statement I:
Total students = 16
Crayon or sketch pen = 5 + 5 = 10
Probability that a student is a boy = 9/16
Given a student is a boy, probability he gets crayon or sketch pen = 10/16 = 5/8 (assuming uniform distribution)
Thus, P (boy &cap; crayon/sketch) = 9/16 &times; 10/16 = 90/256 = 45/128
So, Statement I is incorrect
Favourable outcomes for Statement II:
Girls = 7
Markers = 6
Probability = 7/16 &times; 6/16 = 42/256 = 21/128.
Statement II is correct
Hence, correct option is b.

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E Question 1	⏱ 0
In a class of 16 students (9 boys and 7 girls), the teacher randomly distributes 6 markers, 5 crayons, and 5 sketch pens, giving one item to each student such that each student receives exactly one item. Consider the following statements: Statement I: The probability that a randomly selected student is a boy who receives either a crayon or a sketch pen is 25/96. Statement II: The probability that a randomly selected student is a girl who receives a marker is 21/128. Select the correct answer from the options below: (a) Only Statement I is correct. (b) Only Statement II is correct. (c) Both Statements I and II are correct. (d) None of the Statements is correct.

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