A shipment of TVs contains units that are 70 top quality Thi

A shipment of TVs contains units that are 70% top quality. Thirty percent (30 %) of the TVs are poor quality.

Two TVs are randomly selected from the shipment and tested.

What is the probability that both TVs selected are top Quality?

Enter answer as a decimal rounded to 2 decimal places with a 0 to the left of the decimal point.
Do not enter answer as a percent.

What is the probability that one of or more of the TVs are top quality?

Enter answer as a decimal rounded to 2 decimal places with a 0 to the left of the decimal point.
Do not enter answer as a percent.

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 = 2 ) = ( 2 2 ) * ( 0.7^2) * ( 1 - 0.7 )^0
= 0.49

b)

P( X < 1) = P(X=0)
= ( 2 0 ) * 0.7^0 * ( 1- 0.7 ) ^2   
= 0.09
P( X > = 1 ) = 1 - P( X < 1) = 0.91