Question

1. Consider the box: [0,2,3,4,6]

a.) If 2 tickets are drawn at random without replacment from this box, what is the probability that the sum of the draws is equal to 6?

b.) If 400 tickets are drawn at random with replacment from this box, what is the approximate probability that the average of the draws is between 3.1 and 3.2?

Answer 1

a)

number of ways to draw 2 tickets out of 5 =5*4=20

number of ways sum is equal to 6 =5 {(0,6),(6,0),(2,4),(4,2),(3,3)}

hence probability that the sum of the draws is equal to 6 =5/20=0.25

b)

here mean value of a ticket E(X)=(0+2+3+4+6)/5=3

E(X²)=(0²+2²+3²+4²+6²)/5=13

Std deviation =sqrt(E(X²)-(E(X))²)=2

here expected mean of 400 tickets =3

and std deviiton =2/sqrt(400)=0.1

from normal approximation

probability that the average of the draws is between 3.1 and 3.2 =P(3.1<X<3.2)

=P((3.1-3)/0.1<Z<(3.2-3)/0.1)=P(1<Z<2)=0.9772-0.8413=0.1359