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Abhishek

· started a discussion

· 1 Months ago

Question asking odd against the different colour . check it.

Question:
A bag contains 5 black and 6 white balls. If two balls are drawn together at random, what are the odds against being of different colours.
Options:
A) 5 : 6
B) 6 : 5
C) 5 : 11
D) 6 : 11
E) 11 :5
Solution:

Ans: (a) 5 : 6

Odds against being of different 

Colours = \(\cfrac{Probability\ of\ being \ Same \ colours\ }{Probability \ of \ being \ different \ colour}\)

\(\cfrac{\cfrac{= 5C_2 + 6C_2}{11C_2}}{\cfrac{5C_1 × 6C_1}{11C_2}}\)

= \(\cfrac{5C_2 + 6C_2}{5C_1 × 6C_1}\)

= \(\cfrac{\cfrac{5 × 4}{ 1 × 2} \ \ +\ \cfrac{6 × 5}{1× 2 }}{5 × 6}\)

= \(\cfrac{5}{6}\)

= 5 : 6 

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