Probability
Assam 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
Two coins are tossed simultaneously. Which of the following events are independent?
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First coin shows head and second coin shows head, First coin shows head and second coin shows tail
Independent events are those where the occurrence of one doesn't affect the other. The result of the first coin doesn't influence the second coin, so options 1 and 2 are correct. Options 3 and 4 involve dependencies between the events.
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.
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