Out of every 100 jobs

**zorro** · December 17th 2009, 04:54 PM

Question : Out of every 100 jobs received at a computing center, 50 are of class1, 30 of class 2 and 20 from class 3

i) A sample of 30 jobs is taken without replacement. Find the probability that the sample will contain 10 jobs of each class.

ii) A sample of 3 jobs is taken with replacement, find the probability that there will be exactly 12 jobs of class 2

**Soroban** · December 17th 2009, 05:23 PM

Hello, zorro!

Out of every 100 jobs received at a computing center:
50 are of class 1, 30 of class 2 and 20 of class 3.

i) A sample of 30 jobs is taken without replacement.
Find the probability that the sample will contain 10 jobs of each class.

Answer: . $\frac{{50\choose10}{30\choose10}{20\choose10}}{{10 0\choose30}}$

ii) A sample of 30 jobs is taken with replacement.
Find the probability that there will be exactly 12 jobs of class 2

Answer: . ${30\choose12}(0.3)^{12}(0.7)^8$

**zorro** · December 17th 2009, 05:46 PM

Originally Posted by Soroban

Hello, zorro!

Answer: . $\frac{{50\choose10}{30\choose10}{20\choose10}}{{10 0\choose30}}$

Answer: . ${30\choose12}(0.3)^{12}(0.7)^8$

how did u get $(0.3)^{12}(0.7)^8$

**mr fantastic** · December 18th 2009, 03:02 AM

Originally Posted by zorro

how did u get $(0.3)^{12}(0.7)^8$

It follows a binomial distribution. Tick the boxes for each criterion:

1. Only two possible outcomes: Class 2 (success) and not class 2 (failure).

2. 30 independent trials: n = 30.

3. Probability of success in each trial stays the same: p = 30/100 (because it's sampling with replacement).

**zorro** · December 18th 2009, 01:13 PM

Originally Posted by mr fantastic

It follows a binomial distribution. Tick the boxes for each criterion:

1. Only two possible outcomes: Class 2 (success) and not class 2 (failure).

2. 30 independent trials: n = 30.

3. Probability of success in each trial stays the same: p = 30/100 (because it's sampling with replacement).

I also though it was binomial but i couldnt understand how he got $(0.7)^8$ could u please explain me from where did he get 8 from n-x = 30 - 12 = 18

**mr fantastic** · December 18th 2009, 03:16 PM

Originally Posted by zorro

I also though it was binomial but i couldnt understand how he got $(0.7)^8$ could u please explain me from where did he get 8 from n-x = 30 - 12 = 18

You're correct. Soroban made a typo. (Note: There is also a typo in your original question which Soroban fixed in his quote ....).

**zorro** · December 18th 2009, 06:34 PM

Originally Posted by mr fantastic

You're correct. Soroban made a typo. (Note: There is also a typo in your original question which Soroban fixed in his quote ....).

thanks Mr fantastic and Soroban for helping me with the question
cheers guys

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Out of every 100 jobs

Thanks Soroban

I confusion

Thanks for justifying

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