tennis ball problem!

• Apr 11th 2008, 02:14 AM
matty888
tennis ball problem!
A company that manufactures tennis balls operates three shifts each day. Based on past experience, it is known that a percentage of the balls produced will be defective. The following table shows the percentage produced on each shift and the percentage of defectives in each shift:
Shift Percentage Percentage
Produced of Defectives
1 30% 10%
2 50% 15%
3 20% 20%

If a tennis ball is chosen at random and found to be defective, what is the probability that it was produced on the first shift?
• Apr 11th 2008, 02:34 AM
janvdl
Quote:

Originally Posted by matty888
A company that manufactures tennis balls operates three shifts each day. Based on past experience, it is known that a percentage of the balls produced will be defective. The following table shows the percentage produced on each shift and the percentage of defectives in each shift:
Shift Percentage Percentage
Produced of Defectives
1 30% 10%
2 50% 15%
3 20% 20%

If a tennis ball is chosen at random and found to be defective, what is the probability that it was produced on the first shift?

Use Bayes' Rule

$\displaystyle P(S_1 | D) = \frac{P(D | S_1)P(S_1)}{P(D | S_1)P(S_1) + P(D | S_2)P(S_2) + P(D | S_3)P(S_3)}$

$\displaystyle P(S_1 | D) = \frac{(0,1)(0,3)}{(0,1)(0,3) + (0,15)(0,5) + (0,2)(0,2)}$

$\displaystyle P(S_1 | D) = \frac{6}{29}$

EDIT: Approximately 21%
• Apr 11th 2008, 04:05 AM
mr fantastic
Quote:

Originally Posted by matty888
A company that manufactures tennis balls operates three shifts each day. Based on past experience, it is known that a percentage of the balls produced will be defective. The following table shows the percentage produced on each shift and the percentage of defectives in each shift:
Shift Percentage Percentage
Produced of Defectives
1 30% 10%
2 50% 15%
3 20% 20%

If a tennis ball is chosen at random and found to be defective, what is the probability that it was produced on the first shift?

For a quite similar question (with answer), see http://www.mathhelpforum.com/math-he...tml#post128009.
• Apr 11th 2008, 04:08 AM
mr fantastic
Quote:

Originally Posted by janvdl
Use Bayes' Rule

$\displaystyle P(S_1 | D) = \frac{P(D | S_1)P(S_1)}{P(D | S_1)P(S_1) + P(D | S_2)P(S_2) + P(D | S_3)P(S_3)}$

$\displaystyle P(S_1 | D) = \frac{(0,1)(0,3)}{(0,1)(0,3) + (0,15)(0,5) + (0,2)(0,2)}$

$\displaystyle P(S_1 | D) = \frac{6}{29}$

EDIT: Approximately 21%

Ahhhhhhh! And I remember the days when you thought a tree diagram was something you found in a forest .....

You've come a long way in a short time (Yes)
• Apr 11th 2008, 04:45 AM
janvdl
Quote:

Originally Posted by mr fantastic
Ahhhhhhh! And I remember the days when you thought a tree diagram was something you found in a forest .....

You've come a long way in a short time (Yes)

Couldn't have done it without the good people of MHF who are always ready to help. (Handshake) :)

At the moment I am tackling Binomial Distribution and Random Variables... As soon as I get the hang of one thing, another pops up...
• Apr 11th 2008, 04:50 AM
mr fantastic
Quote:

Originally Posted by janvdl
Couldn't have done it without the good people of MHF who are always ready to help. (Handshake) :)

At the moment I am tackling Binomial Distribution and Random Variables... As soon as I get the hang of one thing, another pops up...

Getting off topic a bit but ...... you've heard of the mythical hydra .....!! (Rofl)

You might have noticed that there are a lot of quite good binomial distribution questions scattered across the MHF.