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=0.45​, x<4

Answer 1

Solution :

Given that ,

p = 0.45

1 - p = 1 - 0.45 = 0.55  

n = 9

Using binomial probability formula ,

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

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

  = (9! / (9 - 0)!) * 0.45⁰ * 0.55)^{9 - 8}

  ^{= (9! / ( 9 - 1)!) * 0.451 * 0.55)9 - 7}

  ^{= (9! / (9 - 2)!) * 0.452 * 0.55)9 - 6}

  ^{= (9! / (9 - 3)!) * 0.453 * 0.55)9 - 5}

^{p ( x < 4 ) = 0.3614}

^{Probability = 0.3614}