InterviewSolution
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A bag contains 7 blue towels, 5 green towels, and 8 red towels. Two towels are drawn randomly. What is the probability that both are green?1. 1/382. 1/193. 1/294. 1/185. None of these |
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Answer» Correct Answer - Option 2 : 1/19 Given: Green towel = 5 Blue towel = 7 Red towel = 8 Formula: Probability (E) = Favourable outcomes/Total possible outcomes Note: here, Probability denoted by ‘E’ The formula used for combination is – nCr = n!/(n – r)! × r! Here, n = Sample of items. r = Items are taken at a time. Calculation: Favourable outcomes – 2 (out of 5) 5C2 = 5!/(5 – 2)! × 2! ⇒ 5!/3! × 2! ⇒ 5 × 4 × (3!/3!) × 2! ⇒ 5 × (4/2) × 1 ⇒ 20/2 ⇒ 10 ∴ Favourable outcomes will be 10 Total possible outcomes – 2 (out of 20) 20C2 = 20!/(20 – 2)! × 2! ⇒ (20!/18!) × 2! ⇒ 20 × 19 × (18!/18!) × 2! ⇒ 20 × (19/2) × 1 ⇒ 10 × 19 ⇒ 190 ∴ Total possible outcomes will be 190 Now, Probability (E) = Favourable outcomes/Total possible outcomes Probability (E) = 10/190 ⇒ 1/19 ∴ The Probability that both are green will be 1/19 |
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