A mathmatical question(mistake/paradox)about the probability

Question:There are 8 people. Two of them are above 45 years old the others are under 45. Now we randomly choose two of them. What is the probability of choosing a person above 45 when we already know that another person is under 45?

Solution 1: We know that one of them is under 45so we take one from those six people. Now we have 2 above 45 and 5 under. So the probability is 2/7.

But someone write a solution with conditional probability: P(B|A)=P(AB)/P(A), to this situation,

P(Choose one under 45)=3/4

P(Choose one under 45 and one above 45)=(C(6,1)*C(2,1))/C(8,2)=3/7 So the solution is (3/7)/(3/4)=4/7

I can feel this solution have a mistake at the number 3/7 because it does't have any restriction on the sequence of choosing the people, but actually it has. The problem is, its mathematical expression seems flawless, I cannot find the mistake or write another correct one.

I would appreciate it if someone can find its problem in the math theory or write a correct one(Better with math expression.)

Note by Thomas Yao
2 years, 3 months ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}


Sort by:

Top Newest

It's right, it's just Hypergeometric Distribution.

Pi Han Goh - 2 years, 2 months ago

Log in to reply


Problem Loading...

Note Loading...

Set Loading...