Match List - I with List - II.
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List - I
(Queries)
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List II
(Probability)
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A.
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A bag contains 6 white and 4 red balls. Two balls are drawn at random. What is the chance, they will be the same colour?
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I.
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3/68
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B.
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In a pack of 52 cards, one card is drawn at random, what is the probability that it is either a king or a queen ?
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II.
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14/68
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C.
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A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 1 red and 2 white balls?
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III.
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2/13
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D.
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A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random. Find the probability of 2 blue and 1 red balls?
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IV.
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7/15
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Choose the correct answer from the options given below:
1.(A) - (III), (B) - (IV), (C) - (I), (D) - (II)
2.(A) - (III), (B) - (IV), (C) - (II), (D) - (I)
3.(A) - (IV), (B) - (III), (C) - (II), (D) - (I)
4.(A) - (IV), (B) - (III), (C) - (I), (D) - (II) ✓ Correct
Solution
The correct answer is A - IV, B - III, C - I, D - II
Solution Statement
- A. A bag contains 6 white and 4 red balls. Two balls are drawn at random. What is the chance, they will be the same colour?
- Total number of ways to draw 2 balls out of 10 balls = C(10, 2) = 45.
- Number of ways to draw 2 white balls = C(6, 2) = 15.
- Number of ways to draw 2 red balls = C(4, 2) = 6.
- Probability of drawing 2 balls of the same color = (15 + 6) / 45 = 21 / 45 = 7 / 15.
- So, A matches with IV.
- B. In a pack of 52 cards, one card is drawn at random, what is the probability that it is either a king or a queen?
- There are 4 kings and 4 queens in a pack of 52 cards.
- Total number of favorable outcomes = 4 + 4 = 8.
- Probability = 8 / 52 = 2 / 13.
- So, B matches with III.
- C. A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability of 1 red and 2 white balls?
- Total number of ways to draw 3 balls out of 18 balls = C(18, 3) = 816.
- Number of ways to draw 1 red ball = C(6, 1) = 6.
- Number of ways to draw 2 white balls = C(4, 2) = 6.
- Probability = (6 * 6) / 816 = 36 / 816 = 3 / 68.
- So, C matches with I.
- D. A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random. Find the probability of 2 blue and 1 red balls?
- Total number of ways to draw 3 balls out of 18 balls = C(18, 3) = 816.
- Number of ways to draw 2 blue balls = C(8, 2) = 28.
- Number of ways to draw 1 red ball = C(6, 1) = 6.
- Probability = (28 * 6) / 816 = 168 / 816 = 14 / 68.
- So, D matches with II.
Therefore, the correct option is A - IV, B - III, C - I, D - II. So, the correct option is 4).
