The CAT QA section requires speed and accuracy, along with a thorough understanding of the Probability. This article provides a set of MCQs on Probability to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
Also Read
CAT MCQs on Probability
1. Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is
A
20
B
22
C
19
D
21
2. In a box there are (x + 5) red balls, ‘x’ blue balls and (x + 1) black balls. If the probability of picking two blue balls at random is 1/35, then find the value of ‘x’.
A
4
B
2
C
5
D
3
3. A bag contains some red, some green and 9 blue balls. Ratio of number of red to green ball in the bag is 5:4. If the probability of drawing a red ball is \(\frac{1}{6}\) more than that of drawing a blue ball then find the probability of getting three different coloured ball when three balls are drawn from the bag one after another and without replacement.
A
\(\frac{27}{119}\)
B
\(\frac{9}{238}\)
C
\(\frac{18}{119}\)
D
\(\frac{54}{119}\)
4. A bag contains 3 red, 4 white, and 5 blue balls. Two balls are drawn at random. What is the probability that both are of the same color?
A
\( \frac{19}{66} \)
B
\( \frac{17}{66} \)
C
\( \frac{15}{66} \)
D
\( \frac{13}{66} \)
5. What is the probability of getting a sum of 7 when two dice are rolled?
A
\( \frac{1}{6} \)
B
\( \frac{1}{12} \)
C
\( \frac{1}{9} \)
D
\( \frac{1}{36} \)
6. A bag contains 4 red, 3 white, and 2 blue balls. Two balls are drawn at random. What is the probability that both are red?
A
\( \frac{1}{6} \)
B
\( \frac{1}{12} \)
C
\( \frac{1}{9} \)
D
\( \frac{2}{9} \)
7. A bag contains 3 red and 5 black balls. Two balls are drawn at random. What is the probability that both are red?
A
\( \frac{3}{28} \)
B
\( \frac{3}{56} \)
C
\( \frac{1}{14} \)
D
\( \frac{1}{28} \)
8. A and B throw with one die for a stake of Rs. 11 which is to be won by the player who first throws a 6. If A has the first throw, what are their respective expectations?
A
Rs. 7, Rs. 4
B
Rs. 6, Rs. 5
C
Rs. 4, Rs. 7
D
Rs. 5, Rs. 6
9. A bag has 5 red and 7 blue balls. Two balls are drawn without replacement. What is the probability both are red?
A
\( \frac{5}{33} \)
B
\( \frac{10}{66} \)
C
\( \frac{5}{66} \)
D
\( \frac{10}{33} \)
10. A die is rolled twice. What is the probability of getting a sum of 9?
A
\( \frac{1}{9} \)
B
\( \frac{1}{12} \)
C
\( \frac{1}{6} \)
D
\( \frac{2}{9} \)
11. If 3x + 4y = 12 and x - y = 1, what is the value of x + y?
A
24/7
B
25/4
C
25/7
D
23/7
12. What is the probability that a leap year has 53 Sundays?
A
\( \frac{1}{7} \)
B
\( \frac{2}{7} \)
C
\( \frac{3}{7} \)
D
\( \frac{4}{7} \)
13. Ten 50 paise coins: 6 tails, 4 heads. One coin is flipped randomly, seven times in total. One coin is covered. The rest show 5 tails and 4 heads. What does the covered coin show?
A
a head
B
a tail
C
more likely a head
D
more likely a tail
14. A box contains 6 red, 7 green, and 5 blue balls (all distinct in size). What is the probability that the selected red ball is the smallest red ball?
A
1/18
B
1/3
C
1/6
D
2/3
15. In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable-TV or VCR?
A
\( \frac{19}{30} \)
B
\( \frac{2}{3} \)
C
\( \frac{17}{30} \)
D
\( \frac{23}{30} \)
Comments