A bag contains 3 red marbles, 4 blue marbles and x green marbles. Given that the probability of choosing 2 green marbles is 5/26 calculate the number of marbles in the bag?

1 Answer
MattyMatty
Mar 4, 2018

#n = 13#

Explanation:

#"Name the number of marbles in the bag, "n.#
#"Then we have"#

#(x/n)((x-1)/(n-1)) = 5/26#
#x = n - 7#
#=> ((n-7)/n)((n-8)/(n-1)) = 5/26#
#=> 26(n-7)(n-8) = 5 n(n-1)#
#=> 21 n^2 - 385 n + 1456 = 0#
#"disc : "385^2 - 4*21*1456 = 25921 = 161^2#
#=> n = (385 pm 161)/42 = 16/3 " or "13#
#"As n is an integer we have to take the second solution (13) : "#

#=> n = 13#

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