Question

The Canadian Centre for Justice Studies reported that 7% of Canadian youth, aged 12 to 17, had been charged with criminal code offences. If 16 Canadian youth are randomly selected, find the probability that at least two have been charged with criminal code offences.

Answer 1

Solution:

Given,

p = 7% = 0.07

1 - p = 1 - 0.07 = 0.93

n = 16

X follows the Binomial(16 , 0.07)

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x} ; x = 0 ,1 , 2 , ....., n

Now ,

P[at least two]

= P[X 2]

= 1 - { P[X < 2] }

= 1 - { P(X = 0) + P(X = 1) }

= 1 - { (₁₆ C ₀) * 0.07⁰ * (0.93)^{16 - 0} +  (₁₆ C ₁) * 0.07¹ * (0.93)^{16 - 1} }

= 1 - {0.31313180171 + 0.3771049655 }

= 0.30976323279