# Probability of selecting defective light bulbs

• mamma_mia66
In summary, the conversation discusses a problem where a box contains 24 light bulbs, 4 of which are defective. One person selects 10 bulbs at random, and a second person takes the remaining 14. The question is what is the probability that all 4 defective bulbs will be obtained by the same person. The solution involves using combinatorial methods and calculating the probability for both scenarios (the first person selecting all 4 defective bulbs and the second person selecting all 4). The final answer is 0.114, and there are two different ways to arrive at this answer.
mamma_mia66

## Homework Statement

A box contains 24 light bulbs of which 4 are defective. If one person selects 10 bulbs from the box in a random manner, and a second person then takes the remaining 14 bulbs, what is the probability that all 4 detective bulbs will be obtained by the same person.?

## Homework Equations

I don't know how to show the solution because I can't find the big parentheses and numbers are one above the other (24 10) 10 from 24 Combinatorial Methods

## The Attempt at a Solution

Here we 24 light bulbs in that 4 aare defectives.

First person takes 10 bulbs from the box that can be done in the (10 form 24) ways.

In that 4 are defective items remeaning are not defective items.

probability that all 4 detective bulbs will be obtained by the same person
Required probability

Last edited:

probability (4 from 4)*(6 from 20)/(10 from 24) + (10 from 20)/(10 from 24).

Does someone know how to write this in form for combinatorial methods. I want to verify my answer.

Looks correct to me. To calculate (24 10) for example; use the $$_n C_r$$ on your calculator: $$24 \ _nC_r \ 10$$.

Probability that the first person selects all the four defective ones:

(4 4)(20 6)/(24 10) = 0.01976

Probability that the second person selects all the four defective ones:

(4 0)(20 10)/(24 10) = 0.09420

Then you can add the two probabilities because they are independent occurences:

P = 0.1140

Last edited:

Thank you. I forgot to check the the answer in the textbook, it is given only :

(20 6) + (20 10) / (24 10).

Thank you again.

where is the remaining 14. In that 4 are defective items remaining are not defective items.
then:

(4 4)(20 6) / (24 10) + (20 10) /(24 14)=0.114

that way answer is the same but not the same in the book.

mamma_mia66 said:
where is the remaining 14. In that 4 are defective items remaining are not defective items.
then:

(4 4)(20 6) / (24 10) + (20 10) /(24 14)=0.114

that way answer is the same but not the same in the book.

Just two different ways of regarding the same problem. The probability of choosing 14 (including all the 4 deficient ones) out of 24, is the same as choosing 10 normal bulbs out of 24.

Thanks.

## 1. What is the probability of selecting a defective light bulb from a batch of 100 bulbs?

The probability of selecting a defective light bulb from a batch of 100 bulbs depends on the number of defective bulbs in the batch. For example, if there are 10 defective bulbs in the batch, the probability would be 10/100 or 10%.

## 2. How do you calculate the probability of selecting a defective light bulb?

To calculate the probability of selecting a defective light bulb, you need to know the total number of bulbs and the number of defective bulbs in the batch. The probability is then calculated by dividing the number of defective bulbs by the total number of bulbs.

## 3. Can the probability of selecting a defective light bulb be higher than 100%?

No, the probability of selecting a defective light bulb cannot be higher than 100%. This is because probability is a measure of likelihood and cannot exceed 100%.

## 4. Is it possible to have a batch of light bulbs with a probability of 0% of selecting a defective bulb?

Yes, it is possible to have a batch of light bulbs with a probability of 0% of selecting a defective bulb. This means that there are no defective bulbs in the batch.

## 5. How does the probability of selecting a defective light bulb change if more bulbs are added to the batch?

The probability of selecting a defective light bulb increases as more bulbs are added to the batch. This is because there are more bulbs in the batch, which increases the likelihood of selecting a defective one.

• Calculus and Beyond Homework Help
Replies
18
Views
1K
• Calculus and Beyond Homework Help
Replies
3
Views
4K
• Calculus and Beyond Homework Help
Replies
1
Views
1K
• Calculus and Beyond Homework Help
Replies
2
Views
3K
• Calculus and Beyond Homework Help
Replies
7
Views
2K
• Precalculus Mathematics Homework Help
Replies
2
Views
1K
• Calculus and Beyond Homework Help
Replies
6
Views
4K
• Calculus and Beyond Homework Help
Replies
1
Views
3K
• Special and General Relativity
Replies
20
Views
2K
• Calculus and Beyond Homework Help
Replies
6
Views
7K