Probability of At Least One Non-Defective Bulb Selected from Company's Stock

[Amith2006]

Homework Statement

A Company manufactures bulb. 4 percent of it are defective. A Supervisor selects 2 bulbs at random. What is the probability that atleast one of the bulb is not defective?

Homework Equations

The Attempt at a Solution

probability of selecting atleast one non defective bulb = 1 - probability of selecting 2 defective bulbs
= 1 - C[4,2]/C[100,2]
= 824/825
IS IT RIGHT?

 

[exk]

Your problem doesn't state how many bulbs were manufactured total so you can't assume it's 100, hence your solution is wrong.

I think the following might work better for you:
Let X= # of defective bulbs. Then you want to find P(X=<1)=P(X=0)+P(X=1)
P(X=0)=.96^2 P(X=1)=2*.04*.96 P(X=<1)=0.9984

 

[mistermath]

What Exk is saying is that the probability of picking a defective item is 4%. Even if you pick a defective item, what's the chance of the next one being defective? 4%! But if you limit yourself to 100 total bulbs, then as you pick bulbs, the probabilities are changing. So in a way, in this particular problem, you have an "infinite" number of bulbs to work with.

What is weird is that both ways have an error associated with it but from the wording it sounds like the book is testing the infinite # of bulbs idea.

 

[exk]

Actually there are specifically 2 bulbs that you are dealing with so when calculating the probabilities you have C(2,0) and C(2,1) which I didn't put explicitly, but are in the calculations I mentioned.

 

[tiny-tim]

Hi Amith2006!

probability of selecting a tleast one non defective bulb = 1 - probability of selecting 2 defective bulbs

So far, so good.

Now, since we can assume that there are a very large number of bulbs, the probabilities for the two bulbs are independent, and so we can multiply them:

probability of selecting 2 defective bulbs

= (probability of selecting 1 defective bulb)(probability of selecting another defective bulb).

 

[Redbelly98]

... we can assume that there are a very large number of bulbs, ...

Good point. If there were only 25 bulbs in total, there would be just 1 defective bulb. Probability of picking 2 defective bulbs is therefore zero in this case.

 

[tiny-tim]

<--- … ooh … look … <---

I've found another bulb! ​