A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.

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Question 12 A box contains 12 balls of which some are red in colour. If 6 more red balls are put in the box and a ball is drawn at random, the probability of drawing a red ball doubles than what it was before. Find the number of red balls in the bag.Given, Total balls in the box = 12 Red balls in the box = x Probability of drawing a red ball = (๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘Ÿ๐‘’๐‘‘ ๐‘๐‘Ž๐‘™๐‘™๐‘ )/(๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘๐‘Ž๐‘™๐‘™๐‘ ) = ๐‘ฅ/12 If 6 more red balls are put in the box, Total number of balls = 12 + 6 = 18 Number of red balls = x + 6 Probability of drawing a red balls = (๐‘ฅ + 6)/18 Given, after adding 6 balls, probability of drawing a red ball is double of what it was before. โˆด New Probability = 2 ร— Old probability (๐‘ฅ + 6)/18 = 2 ร— ๐‘ฅ/12 (๐‘ฅ + 6)/18 = ๐‘ฅ/6 6 [(๐‘ฅ + 6)/18] = ๐‘ฅ (๐‘ฅ + 6)/3 = ๐‘ฅ ๐‘ฅ+6 = 3๐‘ฅ 6 = 3๐‘ฅโˆ’๐‘ฅ 6 = 2๐‘ฅ 2๐‘ฅ = 6 ๐‘ฅ" = " 6/2 ๐‘ฅ = 3 โˆด Number of red balls = x = 3

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.