about 30 of all drivers will flash their lights to warn onco

about 30% of all drivers will flash their lights to warn oncoming traffic of speed trap ahead.

A) what is the probabilty at least one of six drivers wil warn oncoming traffic ?

B) what is the expected number of these six drivers that will warn oncoming traffic of a police speed trap ahead?

C) what is the variance of these six drivers that will warn oncoming traffic of a police speed tap ahead?

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
a)
P( X < 1) = P(X=0)
= ( 6 0 ) * 0.3^0 * ( 1- 0.3 ) ^6   
= 0.118

P( X > = 1 ) = 1 - P( X < 1) = 0.882

b)
Expected Mean = 6*0.30 = 1.8

c)
Standard Deviation ( npq )= 6*0.3*0.7 = 1.1225
Variance = ( npq )= 6*0.3*0.7 = 1.26