Question

Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X>4), n=7, p=0.4

Answer 1

Solution :

Given that ,

p = 0.4

1 - p = 1 -0.4 = 0.6  

n = 7

Using binomial probability formula ,

P(X = x) = ((n! / (n - x)!) * p^x * (1 - p)^{n - x}

^{p (  x >  4 )  = p (x = 4) + p (x = 5) +  p (x = 6 )  +  p (x = 7 )}  

  = (7 / (4 - 4)!) * 0.40⁴ * 0.60)^{3 +}

  ^{= (7! / (4 - 5)!) * 0.405 * 0.60)2 +}

  ^{= (7! / (4 - 6)!) * 0.406 * 0.60)1 +}

  ^{= (7! / ( 4 - 7)!) * 0.407 * 0.60)0 +}

= 0.0962

Probability = 0.0962