# needs urgent help in probability distribution

#### Irum

##### New Member
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Suppose there are 1 million parts which have 1% defective parts i.e 1 million parts have 10000 defective parts. Now suppose we are taking different sample sizes from 1 million like 10%, 30%, 50%, 70%, 90% of 1 million parts and we need to calculate the probability of finding maximum 5000 defective parts from these sample sizes. As 1 million parts has 1% defective parts so value of success p is 0.01 and failure q is 0.99. Now the issue is when we r calculating probability of sample sizes below 50% of 1 million parts, value of probability for finding ≤ 5000 defective parts is always 0, at 50% of 1 million parts it is 0.5 and sample sizes of more than 50% give probability equal to 1. It means we only get three probability values in all sample sizes i.e 0, 0.5, 1. Now the issue is that there are no intermediate values between 0-0.5 or 0.5-1 although sample size is changing linearly. Can someone plz mention the issue in this problem. I will be very grateful

#### dj_johnphillips

##### Member
Now the issue is when we r calculating probability of sample sizes below 50% of 1 million parts, value of probability for finding ≤ 5000 defective parts is always 0
Not sure what you mean here, but as I read this that seems incorrect to me.

For a technically correct answer you could start by reading around "permutations and combinations" as a topic to get a feel for what's going on.
Alternatively if you're happy to accept an approximation (which is quite good for drawing small smaples but less good as your sample gets bigger) binomial and Poisson distributions could be a good read.

JP

#### Irum

##### New Member
Not sure what you mean here, but as I read this that seems incorrect to me.

For a technically correct answer you could start by reading around "permutations and combinations" as a topic to get a feel for what's going on.
Alternatively if you're happy to accept an approximation (which is quite good for drawing small smaples but less good as your sample gets bigger) binomial and Poisson distributions could be a good read.

JP
I have read binomial and possion distribution, infact I am applying binomial distribution here. let me clarify my problem. Actually total parts were 1 million which have 1% defective parts. So defective parts were 10000 in 1 million parts. Now I want to take different sample size from these 1 million parts i.e I m taking 10%, 30%, 50%,70% and 90% of these 1 million parts. Here I want to calculate probability of finding maximum 5000 defective parts from each sample size. Suppose I m taking sample size 10% of 1 million parts which is 100000 parts. Now to calculate probability of finding 5000 defective parts in this sample size is 0 which is found by using binomial distribution where success of finding defective parts p=0.01 (as we have 1% of defective parts in 1 million parts), failure q=0.99, r=5000 and n=100000. Similarly when I take any sample size whose fraction is less than 50% of 1 million parts, probability is always zero. When I take sample size 50% of 1 million parts i.e 500000, probability of finding 5000 defective parts is 0.5 and when I take any sample size above 50% of 1 million parts, probability of finding 5000 defective parts is 1. My issue is that why i m not getting any value between 0-0.5 or 0.5-1 although sample sizes are changing linearly. I think now I make my point clear so can you please answer my question now