A) \[{}^{16}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{10}}{{\left( \frac{3}{4} \right)}^{6}}\]
B) \[{}^{16}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{6}}{{\left( \frac{3}{4} \right)}^{10}}\]
C) \[{}^{12}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{10}}{{\left( \frac{3}{4} \right)}^{6}}\]
D) \[^{12}{{C}_{6}}{{\left( \frac{1}{4} \right)}^{6}}{{\left( \frac{3}{4} \right)}^{6}}\]
Correct Answer: B
Solution :
In Binomial distribution, Variance = npq and Mean = np, Variance \[=3=npq,\] Mean \[=\,4=\,np\] Now, \[q=\frac{3}{4},\,\,p=\frac{1}{4}\] and \[n=16\] Probability of success \[=\,{{\,}^{16}}{{C}_{6}}\,{{\left( \frac{3}{4} \right)}^{10}}\,{{\left( \frac{1}{4} \right)}^{6}}\].
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