From a bag containing 4 white and 5 black balls a man drawn 3 balls at random. What are the odds against these balls being black?
A. $$\frac{{5}}{{37}}$$
B. $$\frac{{37}}{{5}}$$
C. $$\frac{{11}}{{13}}$$
D. $$\frac{{13}}{{37}}$$
Answer: Option B
Solution(By Examveda Team)
Probability of all three balls being black$$\eqalign{ & = \frac{{^5{C_3}}}{{^9{C_3}}} \cr & = \frac{5}{{42}} \cr} $$
Probability that three balls are not black
$$\eqalign{ & = 1 - \frac{5}{{42}} \cr & = \frac{{37}}{{42}} \cr} $$
Hence, odds against these ball being black
$$\eqalign{ & = \left( {\frac{{37}}{{42}}} \right):\left( {\frac{5}{{42}}} \right) \cr & = 37:5 \cr} $$
Related Questions on Probability
A. $$\frac{{1}}{{2}}$$
B. $$\frac{{2}}{{5}}$$
C. $$\frac{{8}}{{15}}$$
D. $$\frac{{9}}{{20}}$$
A. $$\frac{{10}}{{21}}$$
B. $$\frac{{11}}{{21}}$$
C. $$\frac{{2}}{{7}}$$
D. $$\frac{{5}}{{7}}$$
A. $$\frac{{1}}{{3}}$$
B. $$\frac{{3}}{{4}}$$
C. $$\frac{{7}}{{19}}$$
D. $$\frac{{8}}{{21}}$$
E. $$\frac{{9}}{{21}}$$
What is the probability of getting a sum 9 from two throws of a dice?
A. $$\frac{{1}}{{6}}$$
B. $$\frac{{1}}{{8}}$$
C. $$\frac{{1}}{{9}}$$
D. $$\frac{{1}}{{12}}$$
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