I have these problems to turn in for tomorrow. I don't know the best way to solve them.
Please see if you can solve them and post your results along with calculations.

Problem 1:

In bowl A there are 4 red balls, 3 blue balls and 2 green balls.
In bowl B there are 2 red, 3, blue and 4 green.
One ball is taken from bowl A and put into bowl B.
After this is done one ball is taken from bowl B.
What are the odds that the ball, taken from bowl B, is red?

Problem 2:

Given are:

S1 = {1,2,3,4}
S2 = {1,2,3,4,5,6}
S3 = {1,2,3,4,5,6,7,8}

We pick one number randomly from S1, where there is an equal chance of picking any one number. We do the same with S2 and S3.
What are the odds that the sum of the numbers we picked are equal to 5?

2. Hello Lesarinn

Welcome to Math Help Forum!
Originally Posted by Lesarinn
I have these problems to turn in for tomorrow. I don't know the best way to solve them.
Please see if you can solve them and post your results along with calculations.

Problem 1:

In bowl A there are 4 red balls, 3 blue balls and 2 green balls.
In bowl B there are 2 red, 3, blue and 4 green.
One ball is taken from bowl A and put into bowl B.
After this is done one ball is taken from bowl B.
What are the odds that the ball, taken from bowl B, is red?
There are two different cases to consider:

• (i) The ball taken from bowl A is red; and then the ball taken from bowl B is red.

• (ii) The ball taken from bowl A is not red; and then the ball taken from bowl B is red.

Work out the probabilities $p_1$ and $p_2$ that the ball taken from A is (i) red, and (ii) not red. Then, by considering the number of red balls in bowl B in each case (i) and (ii), work out the probabilities $q_1$ and $q_2$ that the second ball is red.

Finally, multiply $p_1$ by $q_1$; multiply $p_2$ by $q_2$; then add your answers to get the final answer. I reckon this comes out as $\frac{11}{45}$.

Problem 2:

Given are:

S1 = {1,2,3,4}
S2 = {1,2,3,4,5,6}
S3 = {1,2,3,4,5,6,7,8}

We pick one number randomly from S1, where there is an equal chance of picking any one number. We do the same with S2 and S3.
What are the odds that the sum of the numbers we picked are equal to 5?

Work out all the ways in which the total could be 5; then work out the probability that each of these sequences of numbers occurs. Finally add all your answers together to get the overall probability.

I'll start you off. We could have:

• 1,1,3. The probability of this is $\tfrac14\times\tfrac16\times\tfrac18 = \tfrac{1}{192}$.

• 1,2,2. The probability of this is exactly the same: $\tfrac14\times\tfrac16\times\tfrac18 = \tfrac{1}{192}$

• ... and so on.

I reckon that the answer is $\tfrac{5}{192}$.

Can you complete these now?