- #1

Rikudo

- 120

- 26

- Homework Statement
- There are 2 boxes. box A contains 20 white balls and 20 black balls. Box B contains 10 white balls and 5 black balls. A box is chosen at random, then a ball is taken at random from the chosen box. What is the probability that the ball is white?

- Relevant Equations
- ##P = \frac {n(A)}{n(S)}##

https://www.physicsforums.com/threa...-random-from-a-randomly-selected-box.1034377/

First of all, I would like to point out that this is the same exact question from what is being discussed in the thread above.

In that thread, the problem is solved by adding the probability of taking white from box 1 and taking white from box 2.

Now, I am trying to solve this problem with a different and straightforward way.

We all know that probability is the ratio of the number of favorable outcomes ##n(A)## to the total number of outcomes ##n(S)##of an event.

Or, simply put: $$P = \frac {n(A)}{n(S)}$$

So, let's find the quantity of those two variables.

1. Find ##n(A)##

This one is obvious. This is just the total number of white balls in both box. So, $$n(A)= 20+10=30$$

2. Find ##n(S)##

Now, this one is quite complicated. First, we can choose the 1st box and then choose ANY balls from both boxes. Second, we can choose the 2nd box and then choose ANY balls from both boxes.

So, $$n(S) = the\,number\,of\,box \,\,X\,\,Total\, number \,of \,balls = 2 (20+20+10+5) = 110$$

Hence, the answer is $$P = \frac {30} {110}$$

But, this is not the correct answer. What mistakes did I make?

First of all, I would like to point out that this is the same exact question from what is being discussed in the thread above.

In that thread, the problem is solved by adding the probability of taking white from box 1 and taking white from box 2.

Now, I am trying to solve this problem with a different and straightforward way.

We all know that probability is the ratio of the number of favorable outcomes ##n(A)## to the total number of outcomes ##n(S)##of an event.

Or, simply put: $$P = \frac {n(A)}{n(S)}$$

So, let's find the quantity of those two variables.

1. Find ##n(A)##

This one is obvious. This is just the total number of white balls in both box. So, $$n(A)= 20+10=30$$

2. Find ##n(S)##

Now, this one is quite complicated. First, we can choose the 1st box and then choose ANY balls from both boxes. Second, we can choose the 2nd box and then choose ANY balls from both boxes.

So, $$n(S) = the\,number\,of\,box \,\,X\,\,Total\, number \,of \,balls = 2 (20+20+10+5) = 110$$

Hence, the answer is $$P = \frac {30} {110}$$

But, this is not the correct answer. What mistakes did I make?