Through a mix-up on the production line, 21 defective ovens were shipped out with 29 good ones. If 8 are selected at random, what is the probability that none of them are defective?
need help ASAP
50 shipped
first one ok 29/50
second one 28/49
third one 27/48
etc down to eight of them
then multiply
thank you
To find the probability that none of the selected ovens are defective, we need to know the total number of ovens and the number of defective ovens. Let's break it down step by step:
Step 1: Calculate the total number of ovens
Since there were 21 defective ovens and 29 good ones, the total number of ovens is 21 + 29 = 50.
Step 2: Calculate the number of ways to select 8 ovens out of 50
We can use the combination formula to calculate this. The formula for calculating combinations is nCr = n! / (r!(n-r)!), where n is the total number of objects and r is the number of objects to be selected. In this case, we want to select 8 ovens out of 50, so the number of ways to select is 50C8 = 50! / (8!(50-8)!) = (50*49*48*47*46*45*44*43) / (8*7*6*5*4*3*2*1) = 10272278170.
Step 3: Calculate the number of ways to select 8 good ovens out of the 29 good ovens
We can use the same combination formula, but this time we have 29 good ovens to choose from. So the number of ways to select 8 good ovens is 29C8 = 29! / (8!(29-8)!) = (29*28*27*26*25*24*23*22) / (8*7*6*5*4*3*2*1) = 74974368.
Step 4: Calculate the probability
The probability of selecting 8 good ovens can be calculated by dividing the number of ways to select 8 good ovens by the number of ways to select 8 ovens overall. So the probability is 74974368 / 10272278170 = 0.00729 (rounded to five decimal places).
Therefore, the probability that none of the selected ovens are defective is approximately 0.00729 or 0.729%.