Question

A box contains 12 balls of which some are red in colour .If 6more 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.

Answer 1

here let the no. of red balls be x. now probability of getting red ball P, = x/12
again when 6 more are added, the new probability, P1 = x/18 , (12+6)
also x+6/18 = 2x/12 according to question. therefore x = 3

Answer 2

HEY BUDDY..!!!

HERE'S THE ANSWER..

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♠️ P1 = Portability of getting red ball

⏺️ Total balls in bag = 12

⏺️let number of red balls be ( x )

✔️ { Probability = favourable outcomes / total outcomes }

♠️ P1 = number of red balls / total balls

=> [ P1 = x / 12 ]

▶️ After adding 6 more red balls

⏺️ number of red balls = x + 6

⏺️ total number of ball = 12 + 6 = 18

▶️P2 = probability of getting red balls after adding 6 red balls

♠️ [ P2 = ( x + 6 ) / 18 ]

▶️ Now , 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

⏺️ According to this statement

♠️ 2 × P 1 = P 2

⏺️ Now putting the values

=> 2 × P 1 = P 2

=> 2 ( x / 12 ) = ( x + 6 ) / 18

=> x / 6 = ( x + 6 ) / 18

=> x = 6 ( x + 6 ) / 18

=> x = ( x + 6 ) / 3

=> 3 x = x + 6

=> 3 x - x = 6

=> 2 x = 6

=> [ x = 3 ] ✔️✔️

♠️ So the total number of red ball is 3 ( before adding 6 balls )

HOPE HELPED..

JAI HIND..

:-)