Question

In the past year, 13% of businesses have eliminated jobs. If 7 businesses are selected at random, find the probability that at least 4 have eliminated jobs during the last year. Round you answer to four decimal places.

P(at least 4 have eliminated jobs during the last year) = _________

Answer 1

Solution :

Given that ,

p = 0.13

1 - p = 1 - 0.13 = 0.87

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 - 3)!) * 0.13⁴ * 0.87)^{3 +}

⁼ (7! / (5 - 2)!) * 0.13⁵ * 0.87)² +

= (7! / ( 6 - 1)!) * 0.13⁶ * 0.87)¹ +

   = (7! / (7 - 0)!) * 0.13⁷ * 0.87)⁰ +

p (  x 4 )  = 0.0072

Probability = 0.0072