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A bag contains 4 red, 5 yellow and 6 pink balls. Two balls are drawn at random. What is the probability that none of the balls drawn are yellow in colour?
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A) \( \Large \frac{1}{7} \) |
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B) \( \Large \frac{3}{7} \) |
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C) \( \Large \frac{2}{7} \) |
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D) \( \Large \frac{5}{14} \) |
Correct Answer:
| B) \( \Large \frac{3}{7} \) |
Description for Correct answer:
Total number of balls in the bag = 4 + 5 + 6 = 15
Total possible outcomes = Selection of 2 balls out of 15balls
= \( \Large ^{15}C_{2} = \frac{15 \times 14}{1 \times 2} = 105 \)
Total favourable outcomes = Selection of 2 balls out of 4 orange and 6 pink balls
= \( \Large ^{10}C^{2} = \frac{10 \times 9}{1 \times 2} = 45 \)
Therefore, Required probability = \( \Large \frac{45}{105} = \frac{3}{7} \)
Total number of balls in the bag = 4 + 5 + 6 = 15
Total possible outcomes = Selection of 2 balls out of 15balls
= \( \Large ^{15}C_{2} = \frac{15 \times 14}{1 \times 2} = 105 \)
Total favourable outcomes = Selection of 2 balls out of 4 orange and 6 pink balls
= \( \Large ^{10}C^{2} = \frac{10 \times 9}{1 \times 2} = 45 \)
Therefore, Required probability = \( \Large \frac{45}{105} = \frac{3}{7} \)
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