Asked by Jeff
A manufacturer of light bulbs knows that 3% of the production of their 60W bulbs will be defective. What is the probability that exactly 5 bulbs in a carton of 144 will ne defective?
Did not understand the posted answer before, need it simplified.
Did not understand the posted answer before, need it simplified.
Answers
Answered by
Reiny
One way for your problem could be
DDDDDGGG...GG , with 139 G's, where D stands for "defective" and is .03 and G stands for "good" and G is .97)
the prob of that particular case would be
(.03)^5 (.97)^139
but...
there are many ways to arrange DDDDDGGG...GG
There are 144 elements to arrange, 5 are alike of one kind, and 139 are alike of another.
The number of such ways = 144!/(5!139!)
That is how drwls got his answer of
(0.03)^5*(0.97)^139*144!/(139!*5!)
(I had .16735)
DDDDDGGG...GG , with 139 G's, where D stands for "defective" and is .03 and G stands for "good" and G is .97)
the prob of that particular case would be
(.03)^5 (.97)^139
but...
there are many ways to arrange DDDDDGGG...GG
There are 144 elements to arrange, 5 are alike of one kind, and 139 are alike of another.
The number of such ways = 144!/(5!139!)
That is how drwls got his answer of
(0.03)^5*(0.97)^139*144!/(139!*5!)
(I had .16735)