| Direction: Study the following information carefully and answer the question given below: |
| In a bag, there are some balls of three different colours, i.e. red, green and blue. The number of blue balls is 10 while the probability of getting a green ball is \[\frac{1}{2}\] and the probability of getting a red ball is\[\frac{2}{9}\]. |
A) \[\frac{1}{35}\]
B) \[\frac{8}{63}\]
C) \[\frac{1}{70}\]
D) \[\frac{8}{35}\]
E) \[\frac{6}{47}\]
Correct Answer: B
Solution :
Let the number of Green, Red and Blue balls be = x, y and z respectively. Probability of having a Green ball is \[\frac{1}{2},\] so the no. of Green balls will be equal to the sum of the number of Red balls and Blue balls y + z = x ... (i) Probability of having Red balls (y) = \[\frac{2}{9}\] So, \[\frac{y}{2x}=\frac{2}{9}\] or, \[\frac{y}{x}=\frac{4}{9}\] So, the ratio of Green : Red : Blue \[=9:4:5\] We know that Blue balls are 10 so from that we can derive that Green balls are 18 and Red balls are 8 in a total of 36 balls. According to the question, \[\frac{^{10}{{C}_{1}}\times {}^{8}{{C}_{1}}}{{}^{36}{{C}_{2}}}=\frac{10\times 8}{35\times 18}=\frac{8}{63}\]
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