Probability

Problem 22 -Each of k jars contains m white and n black balls. A ball is randomly chosen from jar 1 and transferred to jar 2, then a ball is randomly chosen from jar 2 and transferred to jar 3, etc. Finally, a ball is randomly chosen from jar k. Show that the probability that the last ball is white is the same as the probability that the first ball is white, i.e., it is m/(m +n).

For problem 22, use k=5, m=10, n=5. Write a short Python program for problem 22. Provide indented code and comments explaining your solution. Thanks

Solution for problem 22 is below:

Step 1 of 2 Assume that P the probability of the event that a white ball is chosen from ith jar. th Now you can use the total probability theorem to find the probability of the i+1 jar. m +1 m+nm+n+1 1m (1-P) 1+1 m+1 1m Again, in this formula, the initial condition represents the situation which is the probability of the 1m event that a white ball is chosen from 1t jar p,- m+ n Comment Step 2 of 2 A Again, if P the probability of the event that a white ball is chosen from 2nd jar, then m+1 m m+n+1 m+ n Thus, it can be generalized that, P,- Hence, it is showed that the probability that the last ball is white is the same as the probability that the first ball is white that is it is m+ n 1m mt n Step 1 of 2 Assume that P the probability of the event that a white ball is chosen from ith jar. th Now you can use the total probability theorem to find the probability of the i+1 jar. m +1 m+nm+n+1 1m (1-P) 1+1 m+1 1m Again, in this formula, the initial condition represents the situation which is the probability of the 1m event that a white ball is chosen from 1t jar p,- m+ n Comment Step 2 of 2 A Again, if P the probability of the event that a white ball is chosen from 2nd jar, then m+1 m m+n+1 m+ n Thus, it can be generalized that, P,- Hence, it is showed that the probability that the last ball is white is the same as the probability that the first ball is white that is it is m+ n 1m mt n