A bag contains 5 blue and an unknown number x of red balls. Two balls are drawn at random. If the probability of both of them being blue is 5 14 , then the value of x is equal to

Question

A bag contains 5 blue and an unknown number x of red balls. Two balls are drawn at random. If the probability of both of them being blue is 5 14 , then the value of x is equal to, 8, 5, 3, 6

MARKS App · Accepted Answer

P = 5 C 2 5 + x C 2 = 5 14 ⇒ 10 × 2 ( 5 + x ) ( 4 + x ) = 5 14 ⇒ x 2 + 20 + 9 x = 14 × 4 ⇒ x 2 + 9 x - 36 = 0 ⇒ x = 3 , - 12

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