find the probability of at least one defective bulb

[sunny1324]

in a lot of 100 bulbs, there are 5 bad bulbs. An inspector inspects 10 bulbs selected at random. Find the probability of finding at least one defective bulb.


I'm not really sure what to do.

here's what I have so far

x = # of defective bulbs in sample size 10 0,1,2,3,4,5

N(s) = 100 C 10
N(x) = 5 C x * 95 C 10-x
P(X=x) = ( 5 C x * 95 C 10-x )/ (100 C 10) x = 0,1,2,3,4,5
P(at least 1 defective) = P(x greater than or equal to 1) = 1-P(x=0)

= 1- ( 5 C 0 * 95 C 10 )/ (100 C 10)

which isn't correct


the answer in the book is 0.416

 

[royhaas]

An elementary way to calculate this is as follows: the probability of drawing the first good bulb is 95/100, the probability of drawing the second is 94/99, and so on, so that the probability of drawing the 10th good bulb is 86/91. Multiply and take the complement.

 

[sunny1324]

oh, so it would be

(95/100)(94/99)(93/98)(92/97)(91/96)(90/95)(89/94)(88/93)(87/92)(86/91) = 0.5837

1-0.5837 = 0.4163



thanks