Question

A binomial probability experiment is conducted with the given parameters. Use technology to find the probability of x successes in the n independent trials of the experiment. n=9, p=0.4, x<4

Answer 1

Solution :

Given that ,

p = 0.4

1 - p = 1 - 0.4 = 0.6  

n = 9

Using binomial probability formula ,

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

So,

P (x < 4 ) =p (x = 0 )+ p (x = 1) + p (x = 2 ) +  p (x = 3 )   

= (9! / (9 - 0)!) * 0.4⁰ * 0.6)^{9 - 8}

  = (9! / (9 - 1)!) * 0.4¹ * 0.6)^{9 - 7}

  = (9! / (9 - 2)!) * 0.4² * 0.6)^{9 - 6}

  = (9! / (9 - 3)!) * 0.4³ * 0.6)^{9- 5}

= 0.4826

Probability =0.4826

P ( x < 4 ) = 0.4826