# Thread: probability question

1. ## probability question

A parking lot contains 100 cars that all look quite nice from the outside.
However, k of these cars happen to be lemons. The integer k is known to lie in the range
{0,1,2,…,9} with all values equally likely.
(a) We testdrive 20 cars chosen at random without replacement, and to our pleasant surprise, none of them turn out to be a lemon. Given this knowledge, what is the probability that k = 0 .
(b) Repeat part (a) when the 20 cars are chosen with replacement.

2. Originally Posted by inneedofhelp
A parking lot contains 100 cars that all look quite nice from the outside.
However, k of these cars happen to be lemons. The integer k is known to lie in the range
{0,1,2,…,9} with all values equally likely.
(a) We testdrive 20 cars chosen at random without replacement, and to our pleasant surprise, none of them turn out to be a lemon. Given this knowledge, what is the probability that k = 0 .
(b) Repeat part (a) when the 20 cars are chosen with replacement.
Use Bayes theorem:

P(k=0| 20 OK) p(20 OK) = P(20 OK|k=0)p(k=0),

you have p(k=0)=1/10, p(20 OK|k=0)=1. So you just need to evaluate:

p(20 OK)= sum[p(20 OK|k=r)p(k=r), r=0 to 9]

RonL