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. Use the Tech Help button for further assistance. n=6​, p=0.650, x<4

Answer 1

Solution :

Given that ,

p = 0.650

1 - p = 1 -0.650 = 0.350  

n = 6

Using binomial probability formula ,

P(X < 4 ) = ((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 )   

  = (6 ! / (6- 0)!) * .0.650⁰ * 0.350 )^{6- 8}

  = (6 ! / (6 - 1)!) * 0.650¹ * 0.350 )^{6- 7}

  = (6 ! / (6 - 2)!) * 0.650² * 0.350 )^{6 - 6}

= (6 ! / (6 - 3)!) * 0.650³ * 0.350 )^{6 - 5}

p ( x < 4 ) = 0.3529

Probability = 0.3529