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Probability - Previous Year Questions

⏱️ Est. Revision Time: 15 Mins
🔍
📅 Year 2024
Q1
CBSE Board Exam 20243 Marks
Two dice are thrown. Find the probability that the sum of the numbers on the dice is (i) 7 (ii) an even number.
▶ Show Detailed Solution
Total outcomes = 36.
(i) Sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 outcomes ⇒ P = 6/36 = 1/6.
(ii) Even sum: odd+odd or even+even = 3×3 + 3×3 = 18 ⇒ P = 18/36 = 1/2.
Q2
CBSE Board Exam 20243 Marks
A die is thrown. If E = {1, 3, 5} and F = {2, 4, 6}, find P(E), P(F) and P(E ∪ F).
▶ Show Detailed Solution
P(E) = 3/6 = 1/2. P(F) = 3/6 = 1/2.
E ∩ F = ∅ ⇒ P(E ∪ F) = P(E) + P(F) = 1/2 + 1/2 = 1.
📅 Year 2023
Q1
CBSE Board Exam 20234 Marks
In a class of 60 students, 30 like cricket, 25 like football and 10 like both. A student is chosen at random. Find the probability that the student likes neither.
▶ Show Detailed Solution
P(C) = 30/60 = 1/2, P(F) = 25/60 = 5/12, P(C ∩ F) = 10/60 = 1/6.
P(C ∪ F) = 1/2 + 5/12 − 1/6 = (6 + 5 − 2)/12 = 9/12 = 3/4.
P(neither) = 1 − 3/4 = 1/4.