Question

We know that 10% people who purchase cars buy manual transmissions and 90% people purchase automatics.Three people purchase a car. find the probability distribution for the number who purchase automatics

Answer 1

Let X be a random variable representing the number who purchase automatics, then X ~ Bin(3, 0.9)

$P(X=0)={3 \choose 0}*0.9^0*0.1^3=0.001$

$P(X=1)={3 \choose 1}*0.9^1*0.1^2=0.027$

$P(X=2)={3 \choose 2}*0.9^2*0.1^1=0.243$

$P(X=3)={3 \choose 3}*0.9^3*0.1^0=0.729$