CAT Exam  >  CAT Tests  >  Test Level 3: Probability - 1 - CAT MCQ

Test Level 3: Probability - 1 - CAT MCQ


Test Description

10 Questions MCQ Test - Test Level 3: Probability - 1

Test Level 3: Probability - 1 for CAT 2024 is part of CAT preparation. The Test Level 3: Probability - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 3: Probability - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 3: Probability - 1 below.
Solutions of Test Level 3: Probability - 1 questions in English are available as part of our course for CAT & Test Level 3: Probability - 1 solutions in Hindi for CAT course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt Test Level 3: Probability - 1 | 10 questions in 20 minutes | Mock test for CAT preparation | Free important questions MCQ to study for CAT Exam | Download free PDF with solutions
Test Level 3: Probability - 1 - Question 1

Two dice are rolled once. What is the probability of getting an even number on the first die or a total of 8?

Detailed Solution for Test Level 3: Probability - 1 - Question 1

P(even number on Ist die or a total of 8) = P(even number on Ist die) + P(total of 8) – P(even number on Ist die and total of 8)
Now, P(even number of Ist die) = 18/36
Ordered pairs showing a total of 8 = {(6, 2), (5, 3), (4, 4), (3, 5), (2, 6)} = 5
∴ P(total of 8) = 5/36
P(even number of Ist die and total of 8) = 3/36

Test Level 3: Probability - 1 - Question 2

If four coins are tossed, then what are the chances of getting two heads and two tails?

Detailed Solution for Test Level 3: Probability - 1 - Question 2

Total number of outcomes = 24 = 16
Number of favourable outcomes = (HHTT), (HTHT), (HTTH), (TTHH), (THTH) and (THHT) = 6
Probability = 6/16 = 3/8

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test Level 3: Probability - 1 - Question 3

Four robbers went to a safe place after a robbery. At midnight, each robber randomly chose one of the other three robbers and shot him. What is the probability that exactly two robbers were shot?

Detailed Solution for Test Level 3: Probability - 1 - Question 3

Let the 4 robbers be A, B, C and D.
Now, A can choose any one out of the 3 robbers to shoot.
Same applies to B, C and D as well.
Thus, total number of ways in which the robbers can shoot each other = 3 × 3 × 3 × 3 = 34
Now, suppose B and C are shot.
So, A can shoot B or C, B can shoot C, C can shoot B, and D again can shoot B or C.
Thus, B and C can be shot in 2 × 2 = 4 ways.
Any two robbers who are selected can be shot in 4 ways.
Also, the number of ways in which the two robbers who are shot can be selected = 4C2
Hence, the total number of ways = 4C2 × 4/34 = 8/27
Thus, answer option 4 is correct.

Test Level 3: Probability - 1 - Question 4

In a dice game, if a player rolls two dice, then his score will be the larger of the two numbers on the dice and if he rolls a doublet, his score will be the same number as the number in doublet. For example, if he rolls 4 and 6, his score will be 6 and if he rolls a doublet, e.g. 3 and 3, then his score will be 3. What is the probability that his score is 4 or more?

Detailed Solution for Test Level 3: Probability - 1 - Question 4

When a player rolls two dice, there are 6 possibilities for the outcome on each dice.
So, there are 36 possibilities for the outcomes when two dice are rolled.
The possibilities that give a score of 3 or less are:
1 and 1, 1 and 2, 1 and 3, 2 and 1, 2 and 2, 2 and 3, 3 and 1, 3 and 2, 3 and 3.
So, 9 of the 36 possibilities give a score of 3 or less and the probability of getting 3 or less = 9/36 = 1/4
Thus, probability of getting 4 or more 

Test Level 3: Probability - 1 - Question 5

Tickets are numbered 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and the other is a multiple of 4.

Detailed Solution for Test Level 3: Probability - 1 - Question 5

No. of tickets numbered from 1 to 10 divisible by 4 = 2
No. of tickets numbered from 1 to 10 divisible by 5 = 2
Let,
Event (A) : No. on one ticket is multiple of 5 and other multiple of 4
P(A) = (First ticket is multiple of 4 and other one of 5) + (First tickets is multiple of 5 and other one of 4)

Test Level 3: Probability - 1 - Question 6

Suppose that 5% of men and 0.25% of women have brown hair. A brown haired person is picked at random. What is the probability of this person being a male? Assume that there are equal number of men and women.  

Detailed Solution for Test Level 3: Probability - 1 - Question 6

E1 = Person selected is a man.
E2 = person selected is a woman.
A = Person selected is brown haired.
P(E1) = P(E2) = 1/2.
P(A/E1) = 5/100 = 1/20.
P(A/E2) = 1/400.

Test Level 3: Probability - 1 - Question 7

A pack of playing cards contains 51 cards instead of 52 cards. The first 13 cards which were examined were all black, the probability that the missing card is red is

Detailed Solution for Test Level 3: Probability - 1 - Question 7

Let A be the event that the 1st 13 cards drawn are all black.
Let B be the event that the missing card is Red.
Let C be the event that the missing card is Black.
By applying Baye's theorem,

Now, when the missing card is Red, we have 26 Black cards and 25 Red cards with 51 cards in total.

Test Level 3: Probability - 1 - Question 8

Directions: Study the following information and answer the given question.

Three friends A, B and C do air rifle shooting as a hobby and compete against each other in friendly competitions. On a Sunday morning, they go to an empty tract of land along with their air rifles to shoot at clay practice targets from the distances of 100 m and 200 m. A hits his target 95% of the times from a distance of 100 m and 70% times from a distance of 200 m. The same figures for B are 85% and 80%, respectively. The same figures for C are 90% and 75%, respectively. They put in numbered chits (1, 2 and 3) to be drawn to decide the order of shooting and then each of them shoots at the targets turn-wise according to the chit number, first from 100 m and then from 200 m. They decide on a point system with 1 point for hitting the target from a distance of 100 m and 2 points for hitting it from a distance of 200 m with the winner getting a round of drinks paid by the other two.

Q. What is the probability that A will win the competition, given that all three of them manage to shoot at their targets from 100 m?

Detailed Solution for Test Level 3: Probability - 1 - Question 8

A will win the competition if A manages to shoot from 200 m and B and C are unable to do so.
Thus, required probability = 0.70(1 - 0.80)(1 - 0.75) = 0.035

Test Level 3: Probability - 1 - Question 9

Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are red or both are jacks?  

Detailed Solution for Test Level 3: Probability - 1 - Question 9

S = Sample space.
n(S) = 52C2 = 1326.
A = event of getting both red cards and B = event of getting both jacks.
(A ∩ B) = event of getting jacks of red cards.
n(A) = 26C2 = 325.
n(B) = 4C2 = 6.
n(A ∩ B) = 2C2 = 1.
P(A) = 325/1326.
P(B) = 6/1326.
P(A ∩ B) = 1/1326.
P(A ∩ B) = P(A) + P(B) – P(A ∩ B) = 330/1326 = 55/221

Test Level 3: Probability - 1 - Question 10

Directions: Read the given information and answer the following:

Two friends A and B play a game of chance. A person tosses a coin and if the coin shows a heads, he rolls a die. He does this twice and the score is the total of the numbers that the die throws up in both the rolls, if at all. If a person ends up with a tails on tossing the coin, he does not roll the die and his score is entered as 0. The winner of the game is the person whose score is the maximum.

Q. What is the probability that B will win with the maximum possible score and A scores 0?

Detailed Solution for Test Level 3: Probability - 1 - Question 10

There shall be one case for the condition in the question to occur:
B scores 6 in both throws and A scores 0.
The probability for this is

Information about Test Level 3: Probability - 1 Page
In this test you can find the Exam questions for Test Level 3: Probability - 1 solved & explained in the simplest way possible. Besides giving Questions and answers for Test Level 3: Probability - 1, EduRev gives you an ample number of Online tests for practice

Top Courses for CAT

Download as PDF

Top Courses for CAT