# Thread: Out of every 100 jobs

1. ## Out of every 100 jobs

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

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

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

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

3. ## Thanks Soroban

Originally Posted by Soroban
Hello, zorro!

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

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

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

4. Originally Posted by zorro
how did u get $\displaystyle (0.3)^{12}(0.7)^8$
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).

5. ## I confusion

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 $\displaystyle (0.7)^8$ could u please explain me from where did he get 8 from n-x = 30 - 12 = 18

6. Originally Posted by zorro
I also though it was binomial but i couldnt understand how he got $\displaystyle (0.7)^8$ 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 ....).

7. ## Thanks for justifying

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