BARC Quiz 6: Solution and Q&A

Quiz 6 - Part 1

1. There are 6 people lining up to pay telephone bills. If two persons don’t want to follow each other, how many different line ups is possible?
2. In how many ways can 5 engineers and 4 nurses be arranged in a round table if the nurses insisted to be sitting side by side?
3. A die is thrown randomly four hundred fifty times. The frequencies of outcomes 1, 2, 3, 4, 5 and 6 were noted as given in the following table:
   

   Outcomes	1	2	3	4	5	6
   Frequency	73	70	74	75	80	78

   Find the probability of the occurrence of the event that a number is greater than 4.

4. A spider eats three flies a day. Until he fills his quota, he has an even chance of catching any fly that attempts to pass. A fly is about to make the attempt. What are the chances of survival, given that five flies have already made the attempt today?

Quiz 6 - Part 2

1. One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white balls and 5 black balls. One ball is drawn at random from the second bag and is placed unseen in the first bag. What is the probability that a ball now drawn from the first bag is black?
2. A magician holds one six-sided die in his left hand and two in his right. What is the probability the number on the dice in his left hand is greater than the sum of the dice in his right?
3. Three marksmen simultaneously shoot and hit a rapidly spinning spherical target. What is the probability that the three points of impact lie on the same hemisphere?

Quiz 6 - Part 3

1. In a family of five children, what is the chance that there are three boys and two girls?
2. A store has three kinds of toys given in every purchase. What is the probability of getting all three toys in five purchases?
3. The probabilities that three men hit a target are 1/6, 1/4, and 1/3, respectively. Each shoot once at the target. If only one of them hits the target, find the probability that it was the first man.