I have two questions that I need help on.
1. Bag M contains 5 white balls and 2 red balls and bag N contains 3 white balls and 4 red balls and you randomly select a ball from Bag M and place it in Bag N. If a white ball is selected from Bag N, what is the probability that a red ball was transferred from Bag M to Bag N.
2. There are 10 horses in a race. A particular bet requires a customer to choose the first three horses in the correct finishing order. If all 10 horses have an equal chance of finishing in any position, determine the probability that a single bet wins.
We have an additional piece of information that we can use: a white ball was selected from bag N.1) P(Red^M)
Before we take the ball out, there is Sengnee's 2/7 chance of there being 5 red balls and 3 white balls (case one), and a 1-2/7=5/7 chance of there being 4 red balls and 4 white balls (case 2).
So taking a white ball out of case one has probability and the probability of taking a white ball out of case 2 is
So knowing we took a white ball out, the probability that a red ball was transferred is the probability of taking a white ball out of case one divided by the total probability of taking out a white ball ie.