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Probability (Easy Level) - CAT MCQ


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12 Questions MCQ Test - Probability (Easy Level)

Probability (Easy Level) for CAT 2024 is part of CAT preparation. The Probability (Easy Level) questions and answers have been prepared according to the CAT exam syllabus.The Probability (Easy Level) MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Probability (Easy Level) below.
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Probability (Easy Level) - Question 1

What is the chance of throwing a number greater than 4 with an ordinary dice whose faces are numbered from 1 to 6? 

Detailed Solution for Probability (Easy Level) - Question 1

We know that the dice has only numbers 5,6 more than 4.
5 or 6 out of a sample space of 1,2,3,4,5 or 6
We also know the probability of having one number is 1/6.
Hence is P (5) or P (6) = 1/6  + 1/6  = 2/6=1/3 

Probability (Easy Level) - Question 2

Find the chance of drawing 2 blue balls in succession from a bag containing 5 red and 7 blue balls, if the balls are not being replaced.

Detailed Solution for Probability (Easy Level) - Question 2

Event definition: First is blue and second is blue = 7/12 X 6/11 = 7/22.

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Probability (Easy Level) - Question 3

100 students appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has failed in both the examinations?

Detailed Solution for Probability (Easy Level) - Question 3


From the figure it is evident that 80 students passed at least 1 exam. Thus, 20 failed both and the required probability is 20/100 = 1/5.

Probability (Easy Level) - Question 4

In rolling two dices, find the probability that there is at least one ‘6’

Detailed Solution for Probability (Easy Level) - Question 4

With a six on the first dice, there are 6 possibilities of outcomes that can appear on the other dice (viz. 6 & 1, 6 & 2, 6 & 3, 6 & 4, 6 &5 and 6&6).At the same time with 6 on the second dice there are 5 more possibilities for outcomes on the first dice: (1 & 6, 2 & 6, 3 & 6, 4 & 6, 5 & 6)
Also, the total outcomes are 36. Hence, the required probability is 11/36.
 

Probability (Easy Level) - Question 5

From a bag containing 4 white and 5 black balls a man draws 3 at random. What are the odds against these being all black?

Detailed Solution for Probability (Easy Level) - Question 5

Odds against an event = p(E’)/p(E)
In this case, the event is: All black, i.e., First is black and second is black and third is black.
P(E) = 5/9 X 4/8 X 3/7 = 60/504 = 5/42.
Odds against the event = 37/5.

Probability (Easy Level) - Question 6

Phoebe throws three dice in a special game of Ludo. If it is known that he needs 15 or higher in this throw to win then find the chance of his winning the game

Detailed Solution for Probability (Easy Level) - Question 6

Event definition is: 15 or 16 or 17 or 18.
15 can be got as: 
5 and 5 and 5 (one way)            
Or
6 and 5 and 4 (Six ways)        
Or 6 and 6 and 3 (3 ways)        
Total of 10 ways. 16can be got as: 6 and 6 and 4 (3ways)
Or 6 and 5 and 5 (3ways) = Total 6 ways.
17 has 3 ways and 18 has 1 way of appearing. Thus, the required probability is: (10 + 6 + 3 + 1)/216 = 20/216 = 5/54. 

Probability (Easy Level) - Question 7

Find out the probability of forming 187 or 215 with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 when only numbers of three digits are formed and when repetitions are not allowed.

Detailed Solution for Probability (Easy Level) - Question 7

Positive outcomes = 2 (187 or 215) Total outcomes = 9 X 8 X 7
Required probability = 2/504

Probability (Easy Level) - Question 8

Two fair dice are thrown. What is the probability that the sum is less than 10?

Detailed Solution for Probability (Easy Level) - Question 8

Sum less than 10 is the non event for the case sum is 10 or 11 or 12. There are 3 ways of getting 10, 2 ways of getting 11 and 1 way of getting a sum of 12 in the throw of two dice. 
Thus, the required probability would be 1 – 6/36 = 5/6.

Probability (Easy Level) - Question 9

In a certain lottery the prize is ` 1 crore and 5000 tickets have been sold. What is the expectation of a man who holds 10 tickets?

Detailed Solution for Probability (Easy Level) - Question 9

Probability of winning X Reward of winning = (10/5000) X 1 crore = (1 crore/500) = 20000.

Probability (Easy Level) - Question 10

A bag contains four black and five red balls. If three balls from the bag are chosen at random, what is the chance that they are all black?

Detailed Solution for Probability (Easy Level) - Question 10

Once a black ball is selected, the probability of black is going to get affected as the number of black balls & total balls decrease by a number of 1 for each removal of blackball.
Black and Black and Black = 4/9 X 3/8 X 2/7 = 24/504 = 1/21.

Probability (Easy Level) - Question 11

A bag contains 20 balls marked 1 to 20. One ball is drawn at random. Find the probability that it is marked with a number multiple of 5 or 7.

Detailed Solution for Probability (Easy Level) - Question 11

Positive Outcomes are: 5, 7, 10, 14, 15 or 20 - which are 6 in number out of 20 balls From the equation of probability, we get 6/20 = 3/10.
 

Probability (Easy Level) - Question 12

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that all the three balls are of the same colour.

Detailed Solution for Probability (Easy Level) - Question 12

The required probability would be given by:
All are Red OR All are white OR All are Blue
= (6/18) X(5/17) X(4/16) + (4/18) X(3/17) X(2/16) + (8/18) X(7/17) X(6/16) 
= 480/(18 X17 X16) = 5/51

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