1. Probability Problems

Hi guys, this is my first post

I received few problems from my teacher and she won't bother explaining it in details. Anyway, here is the problems given:

1) A sack contains 4 balls, one black and the rest is all white. A person is told to take two balls in a random manner, the person directly took two balls and not returning them, which leaves the sack with two balls only. What is the probability that one of the balls taken by the man is a black ball? Express your answer in percentage!

2) 5 Balls are visibly put on a table so that the students can see, each ball had a letter on it: "A", "B", "C", "D", and "E". Using the information told, solve the following:

i) Find the total number of permutations.
ii) If then the balls were put on a sack and 3 balls were taken out randomly, what are the number of combination of the balls and what is the probability that one of the balls taken is ball "B"?

If possible please mention the steps you used to count them,

2. Originally Posted by Procon
Hi guys, this is my first post

I received few problems from my teacher and she won't bother explaining it in details. Anyway, here is the problems given:

1) A sack contains 4 balls, one black and the rest is all white. A person is told to take two balls in a random manner, the person directly took two balls and not returning them, which leaves the sack with two balls only. What is the probability that one of the balls taken by the man is a black ball? Express your answer in percentage!

2) 5 Balls are visibly put on a table so that the students can see, each ball had a letter on it: "A", "B", "C", "D", and "E". Using the information told, solve the following:

i) Find the total number of permutations.
ii) If then the balls were put on a sack and 3 balls were taken out randomly, what are the number of combination of the balls and what is the probability that one of the balls taken is ball "B"?

If possible please mention the steps you used to count them,
(1) Calculate P(BW)+P(WB)=(1/4)(1)+(3/4)(1/3)

Assuming that the ball is drawn one after another without replacement, that person could have drawn a white ball first then a black ball or the other way round so you sum up all the possible cases.

(2) (a) You know this.

(b) You know this too.

Among the 3 balls taken out of 5 balls, what is the probability that one of them is a back ball.

Calculate (3C1)/(5C3)

OR 3!/2! x 1/5 x 2/4

Since the 3 balls drawn (B,B',B') could be arranged in 3!/2! ways.