In a classroom there are 100 pupils, of whom 40 are boys, 30 wear glas

Question

In a classroom there are 100 pupils, of whom 40 are boys, 30 wear glasses, and 15 are boys who wear glasses.
Total T = 100
Boys = 40, Girls = 60
30 wear glasses, 70 don't wear glasses
15 boys wear glasses, 15 girls wear glasses
25 boys don't wear glasses, 45 girls don't wear glasses.

the probability that it is a boy who don't wear glass = 25/70 = 5/14

Answer is D

A. 9/14
B. 11/20
C. 9/20
D. 5/14
E. 2/7

yashikaaggarwal · Answer

In a classroom there are 100 pupils, of whom 40 are boys, 30 wear glasses, and 15 are boys who wear glasses.
Total T = 100
Boys = 40, Girls = 60
30 wear glasses, 70 don't wear glasses
15 boys wear glasses, 15 girls wear glasses
25 boys don't wear glasses, 45 girls don't wear glasses.

the probability that it is a boy who don't wear glass = 25/70 = 5/14

Answer is D

wilsonprj · Answer

P( boy | No glasses)

Students without glasses = 100 - 30 = 70

Boys without glasses 40 - 15 = 25

P ( Boy | No glasses) = 25/70 = 5/14

egmat · Answer

Let's break this down step by step using simple counting.

We're told:
- Total students:  100 
- Boys:  40 
- Wear glasses:  30 
- Boys who wear glasses:  15

The question says: given that the selected student does NOT wear glasses, what's the probability it's a boy?

Step 1:  Find how many students do NOT wear glasses.
Total students minus glasses-wearers =  100  -  30  =  70  students without glasses.

Step 2:  Find how many BOYS do NOT wear glasses.
Total boys minus boys with glasses =  40  -  15  =  25  boys without glasses.

Step 3:  Now here's the key. Since we already KNOW the student doesn't wear glasses, our universe shrinks from  100  to just those  70  non-glasses students. Out of these  70 , how many are boys?  25 .

So the probability =  25 / 70  =  5 / 14 .

Answer: D

The most common mistake here is dividing  25  by  100  (getting  1/4 ) instead of  70 .  But remember — when the problem says "given that" or "if we know that," it's a  conditional probability  question. You must restrict your total to only the group that satisfies the given condition. Here, that group is the  70  students who don't wear glasses, not all  100  students.

General principle:  In  conditional probability , always ask yourself — what is my new total? The condition given in the problem redefines your denominator.

In a classroom there are 100 pupils, of whom 40 are boys, 30 wear glas

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In a classroom there are 100 pupils, of whom 40 are boys, 30 wear glas

Prep Toolkit

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