Question

A jar contains six red balls numbered 1 to 6, and eight green balls numbered 1 to 8. A ball is drawn at random from the jar. Find the following conditional probabilities. (Enter your probabilities as fractions.)

(b) The ball is green, given that it is numbered 7.


(c) The ball is red, given that it has an even number.


(d) The ball has an even number, given that it is red.

Answer 1

would you like help with this?

Answer 2

@jayzdd yes ;)

Answer 3

When you do conditional probability, you have to reduce the sample space.
So for example P(A | B ) , that means we want the probabily of event A given that you reduce the sample space to B. The sample space is the set of all possible events.

(b) The ball is green, given that it is numbered 7.
We are looking for P( green | 7 ) .
The reduced sample space are the balls numbered 7.
The new sample space = { green 7 }
There is only one ball that is numbered 7, and it is green. Therefore the probability is 1 of getting a green ball given that it is seven.

(c) The ball is red, given that it has an even number.
We are looking for P(red | even).
Reduce the sample space to even balls. I have explicitly listed this new sample space.
Sample space = {red 2, red 4, red 6 , green 2, green 4, green 6, green 8 }
Out of these seven balls, what proportion are red? 3/7

(d) The ball has an even number, given that it is red.
Reduce the sample space to even balls. I have explicitly listed this new sample space.
Sample space = { red 1, red 2, red 3, red 4, red 5, red 6}
What proportion are even numbered?
3/6 = 1/2

Answer 4

@jayzdd so part B is 1/7 ?

Answer 5

part b should be 1