Calculating Binomial Probability for Car Color Preferences

[tzx9633]

Homework Statement

Car colour preferences changes over year . In this year , suppose that 10% of the car are randomly selected , let the sample of cars are 20 . Find the probabilities between thre and five cars ( inclusive ) are black ...

I am aksed to do this question using binomial .

Homework Equations

The Attempt at a Solution

I treated it as P ( 3 < x ≤ 5 ) , am i right ?
so , P( x = 4) + P ( x = 5)
=
(20c4) ((0.1)^4) ( 0.9^16) + (20c5) ((0.1)^5) ( 0.9^15) = 0.1217 ,

However , the ans given is = 0.312 , which part of my working is wrong ?

 

[CrzCz]

I treated it as P ( 3 < x ≤ 5 ) , am i right ?
so , P( x = 4) + P ( x = 5)
=
(20c4) ((0.1)^4) ( 0.9^16) + (20c5) ((0.1)^5) ( 0.9^15) = 0.1217 ,

It is supposed to be P( 3 ≤ x ≤ 5 ). For some reason you treated the '5' correct but not the '3'.

So it will be P( x = 3) + P (x = 4) + P ( x = 5 ) = 0.312

 

[tzx9633]

solved !