Question
A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is -
Answer: Option D
Drawing two balls of same color from seven green balls can be done in $${}^7{C_2}$$ ways.
Similarly from eight white balls two can be drawn in $${}^8{C_2}$$ ways.
$$\eqalign{
& P = \frac{{{}^7{C_2}}}{{{}^{15}{C_2}}} + \frac{{{}^8{C_2}}}{{{}^{15}{C_2}}} \cr
& \,\,\,\,\,\,\, = \frac{7}{{15}} \cr} $$
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Drawing two balls of same color from seven green balls can be done in $${}^7{C_2}$$ ways.
Similarly from eight white balls two can be drawn in $${}^8{C_2}$$ ways.
$$\eqalign{
& P = \frac{{{}^7{C_2}}}{{{}^{15}{C_2}}} + \frac{{{}^8{C_2}}}{{{}^{15}{C_2}}} \cr
& \,\,\,\,\,\,\, = \frac{7}{{15}} \cr} $$
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