Short Answer TypeThe probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?
Long Answer TypeA bag contains 15 white and some black balls. If the probability of drawing a black ball from the bag is thrice that of drawing a white ball, find the number of black balls in the bag.
Two different dice are thrown together. Find the probability that the numbers obtained have
(i) even sum, and
(ii) even product
Elementary events associated to the random experiment of throwing two dice are:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6),
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6),
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6),
Total number of elementary events = 6 x 6 = 36.
(i) Let A be the event of getting an even number as the sum.
i.e. 2, 4, 6, 8, 10, 12.
Elementary events favourable to event A are:
(1,1), (1,3), (1,5), (2,2), (2,4), (2,6),
(3,1), (3,3), (3,5), (4,2), (4,4), (4,6),
(5,1), (5,3), (5,5), (6,2), (6,4), (6,6).
Total number of favourable events = 18.
Hence, required probability =
(ii) Let B be the event of getting an even number as the product.
i.e. 2, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36.
Elementary events favourable to event B are:
(1,2), (1,4), (1,6), (2,1), (2,2), (2,3),
(2,4), (2,5), (2,6), (3,2), (3,4), (3,6),
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6),
(5,2), (5,4), (5,6), (6,1), (6,2), (6,3),
(6,4), (6,5), (6,6).
Total number of favourable events = 27.
Hence, required probability = .
Multiple Choice QuestionsShort Answer TypeA number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.
Long Answer TypeA card is drawn from a well shuffled deck of 52 cards. Find the probability of getting
(i) a king of red colour
(ii) a face card
(iii) the queen of diamonds.
Short Answer Type
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