Question

In a Binomial Distribution, if p = q, then P(X=x) is given by?​

Answer 1

Answer:

8. In a Binomial Distribution, if p = q,then P(X = x) is given by? Substituting inP(x)=nCx px q(n-x) we get nCn (0.5)n.

Answer 2

Answer:

If p = q, then P(X = x) is given by  $^nC_x$ $(\frac{1}{2}) ^n$

Step-by-step explanation:

We know that

In a binomial distribution,

P(x) = ⁿCₓ pˣ qⁿ⁻ˣ                                                                              --(i)

where n = the number of trials

           x = number of times a particular outcome is attained

           p = probability of success

           q = probability of failure

We also know that Probability of success + Probability of failure = 1

=> p + q = 1

According to the question, p = q

Therefore,

     p + p = 1                           (as p + q = 1)

=> 2p = 1

=> p = $\frac{1}{2}$  = q                            (as p = q)

Therefore, substituting the value of p and q in equation (i)

=> P(x) = $^nC_x$ $(\frac{1}{2}) ^x$ $(\frac{1}{2})^{n-x}$

           =  $^nC_x$ $(\frac{1}{2}) ^{x+(n-x)}$                (as $x^{n} . x^m = x^{n+m}$)

            =  $^nC_x$ $(\frac{1}{2}) ^n$

      Therefore, if p = q, then P(X = x) is given by  $^nC_x$ $(\frac{1}{2}) ^n$