Probability
Madhya Pradesh Board · Class 12 · Mathematics
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A bag contains 5 red balls and 3 blue balls. Two balls are drawn without replacement. What is the probability that both balls are red?
In a class of 40 students, 25 like mathematics and 20 like physics. If 10 students like both subjects, what is the probability that a randomly selected student likes mathematics given that they like physics?
A die is rolled twice. What is the probability of getting a sum of 7?
In a survey, 60% people read newspaper A, 50% read newspaper B, and 30% read both. What is the probability that a randomly selected person reads at least one newspaper?
Sample Questions
A box contains 4 defective and 6 non-defective items. If 3 items are drawn randomly without replacement, what is the probability that exactly 2 are defective?
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3/10
P(exactly 2 defective) = C(4,2)×C(6,1)/C(10,3) = (6×6)/120 = 36/120 = 3/10. We choose 2 defective from 4 and 1 non-defective from 6, divided by total ways to choose 3 from 10.
Two events A and B are such that P(A) = 0.4, P(B) = 0.6, and P(A∩B) = 0.24. Are A and B independent events?
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Yes
For independent events, P(A∩B) = P(A)×P(B). Check: 0.4×0.6 = 0.24, which equals P(A∩B). Since the condition is satisfied, A and B are independent.
A card is drawn from a standard deck of 52 cards. Given that the card is red, what is the probability that it is a heart?
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1/2
P(Heart|Red) = P(Heart∩Red)/P(Red) = (13/52)/(26/52) = 13/26 = 1/2. Among the 26 red cards, 13 are hearts, so the probability is 13/26 = 1/2.
In a multiple choice test with 4 options per question, what is the probability of getting exactly 2 correct answers out of 3 questions by random guessing?
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9/64
P(exactly 2 correct) = C(3,2)×(1/4)²×(3/4)¹ = 3×(1/16)×(3/4) = 9/64. Using binomial probability with n=3, k=2, p=1/4.
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