# Probability

### A bag contains 15 red balls and 20 black balls

A bag contains 15 red balls and 20 black balls. Each ball is numbered either 1 or 2 or 3. 20% of the red balls are numbered 1 and 40% of them are numbered 3. Similarly, among the black balls, 45% are numbered 2 and 30% are numbered 3. A boy picks a ball at random. He wins if the ball is red and numbered 3 or if it is black and numbered 1 or 2. What are the chances of his winning?

1. 1/2
2. 4/7
3. 5/9
4. 12/13

### Ramesh plans to order a birthday gift for his friend from an online retailer

Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.

Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?

1. 0.004
2. 0.006
3. 0.216
4. 0.994
5. 0.996

### If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability

If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?

1. 1/12
2. 1/6
3. 1/8
4. 1/4

### An unbiased dice is thrown. What is the probability of getting

An unbiased dice is thrown. What is the probability of getting

• (i) an even number
• (ii) a multiple of 3
• (iii) an even number or a multiple of 3
• (iv) an even number and a multiple of 3

### One card is drawn from a pack of 52 cards

One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is:

• (i) an ace
• (ii) red
• (iii) either red or king
• (iv) red and a king

### There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B

There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red?

### The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes

The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes. Rahul has secured 70, 90 and 80 in the first three quizzes. The fourth quiz has ten True-False type questions, each carrying 10 marks. What is the probability that Rahul’s average internal marks for the Economics course is more than 80, given that he decides to guess randomly on the final quiz?

1. 12/1024
2. 11/1024
3. 11/256
4. 12/256

### A dice is rolled twice. What is the probability that the number

A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

1. 5/36
2. 8/36
3. 15/36
4. 21/36
5. None of the above