Probability — Important Questions
CBSE · Class 11 · Applied Mathematics
45 important questions from Probability for CBSE Class 11 Applied Mathematics, with answers. Includes multiple choice and multiple correct questions.
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Important Questions from Probability
In a group of 50 students, 30 like Math and 25 like Science. If 15 students like both subjects, what is the probability that a randomly selected student likes Math given that they like Science?
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3/5
Using conditional probability: P(Math|Science) = P(Math ∩ Science)/P(Science) = (15/50)/(25/50) = 15/25 = 3/5. Step-by-step: students who like both = 15, students who like Science = 25.
Which of the following are properties of probability? (Select all correct answers)
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0 ≤ P(A) ≤ 1 for any event A, P(S) = 1 where S is sample space, P(A) + P(A') = 1, P(∅) = 0
Basic axioms of probability: (1) Probability is between 0 and 1, (2) Sample space has probability 1, (3) Event and its complement sum to 1, (4) Empty set has probability 0. The union formula P(A ∪ B) = P(A) + P(B) only works for mutually exclusive events.
A box contains 4 red, 3 green, and 2 blue marbles. If two marbles are drawn without replacement, what is the probability that both are red?
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4/21
Total marbles = 9. P(1st red) = 4/9. After drawing 1 red, 8 marbles remain with 3 red. P(2nd red|1st red) = 3/8. P(both red) = (4/9) × (3/8) = 12/72 = 4/21.
If A and B are independent events with P(A) = 0.3 and P(B) = 0.5, what is P(A ∩ B)?
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0.15
For independent events, P(A ∩ B) = P(A) × P(B) = 0.3 × 0.5 = 0.15. Independence means occurrence of one event doesn't affect the other's probability.
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Sources & Official References
- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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