A) 6
B) 5
C) 4
D) 3
Correct Answer: C
Solution :
[c] AS give, \[np=4\] and \[npq=3\] [where p is the probability of success and q is the probability of failure for an event to occur, and ?n? is the number of trials] \[\Rightarrow q=\frac{npq}{np}=\frac{3}{4}\] Also, \[p=1-q=1-\frac{3}{4}=\frac{1}{4}\] \[\therefore n=16\] In a binomial distribution, on the value of r for which \[P(X=r)\] is maximum is the mode of binomial distribution. Hence, \[(n+1)p-1\le r\le (n+1)p\] \[\Rightarrow \frac{17}{4}-1\le r\le \frac{17}{4}\Rightarrow \frac{13}{4}\le r\le \frac{17}{4}\] \[\Rightarrow 3.25\le r\le 4.25\] \[\Rightarrow r=4\]
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