IIT JEE Maths Practice Paper – 19 – PYQs- focused on Probability

Part 19 – Probability
This section contains 10 multiple-choice questions from previous IIT JEE exams focused on Probability. These questions are designed to test your understanding of fundamental probability concepts including independent and dependent events, Bayes’ theorem, and conditional probability.

Part 19 – IIT JEE Maths Practice Paper: Probability

Instructions: Each correct answer gives 4 marks. No negative marking. Choose the best answer for each question and click “Submit” to view your score and explanations.

1. Two dice are thrown simultaneously. What is the probability that the sum is divisible by 4?
   a) 1/4
   b) 1/3
   c) 5/18
   d) 1/2


2. A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is either a red card or a king?
   a) 7/13
   b) 4/13
   c) 15/26
   d) 8/13


3. An unbiased coin is tossed 5 times. What is the probability of getting at least 3 heads?
   a) 1/2
   b) 26/32
   c) 5/16
   d) 11/32


4. A bag contains 3 red and 5 black balls. Two balls are drawn without replacement. What is the probability both are black?
   a) 5/14
   b) 5/7
   c) 5/8
   d) 10/21


5. If A and B are two independent events such that P(A) = 1/3 and P(B) = 1/4, then P(A ∪ B) is:
   a) 1/2
   b) 7/12
   c) 1/3
   d) 3/4


6. What is the probability of getting a sum of 7 or 11 when two dice are rolled?
   a) 2/9
   b) 1/6
   c) 1/4
   d) 5/36


7. A and B throw a die alternatively. The one who gets a 6 first wins. If A starts, then what is the probability that A wins?
   a) 5/11
   b) 6/11
   c) 1/2
   d) 7/13


8. If P(E) = 0.3 and P(F) = 0.4 and E and F are mutually exclusive, find P(E ∪ F).
   a) 0.12
   b) 0.7
   c) 1
   d) 0.1


9. If two events A and B are such that P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.3, then P(A|B) is:
   a) 0.3
   b) 0.6
   c) 0.9
   d) 0.5


10. In how many ways can 3 boys and 2 girls be selected from 5 boys and 4 girls?
    a) 40
    b) 60
    c) 100
    d) 10

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