Question

This exercise is about conditional probability.

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.)

a) The ball is red, given that it is numbered 4.




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

Answer 1

The formula for conditional probability is the probability that the event is both A AND B divided by the probability that it is just B.

For a) P(R|4) = P(R AND 4)/P(4). the probability of being both red and numbered 4 is 1/14, while the probability of being numbered 4 is 2/14 or 1/7. Therefore the probability of the ball being red given that it is number 4 is (1/14)/(1/7) or simplified, 7/14 = 1/2

Part B follows the same logic with different numbers

Answer 2

@LastTrainHome22 thank you ;)