A) \[\frac{27}{32}\]
B) \[\frac{5}{64}\]
C) \[\frac{5}{32}\]
D) \[\frac{1}{2}\]
Correct Answer: C
Solution :
[c] Probability of getting a blue ball at any draw \[=p=\frac{10}{20}=\frac{1}{2}\] P [getting a blue ball 4th time in 7th draw] =P [Getting 3 blue balls in 6 draws]\[\times P\][A blue ball in the 7th draw]. \[{{=}^{6}}{{C}_{3}}{{\left( \frac{1}{2} \right)}^{3}}{{\left( \frac{1}{2} \right)}^{3}}.\frac{1}{2}\] \[=\frac{6\times 5\times 4}{1\times 2\times 3}{{\left( \frac{1}{2} \right)}^{7}}=20\times \frac{1}{32\times 4}=\frac{5}{32}\]
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