SOLUTION: A bin contains 75 light bulbs, 5 of which are defective. If 5 light bulbs are randomly selected from the bin with replacements, find the probability that all the bulbs selected ar

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Question 1178826: A bin contains 75 light bulbs, 5 of which are defective. If 5 light bulbs are randomly selected from the bin with replacements, find the probability that all the bulbs selected are good. Round to three decimal places as needed. What equation would I use to find the answer?
Answer by ikleyn(52811)   (Show Source): You can put this solution on YOUR website!
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It means that you, actually, select your bulbs from the set of 70 good bulbs.


Therefore, you may find the probability as


    P =  = 0.70124  (rounded).    ANSWER


The formula says that you first select any of 70 good bulbs from the total of 75 bulbs;

then you select any of 69 remaining good bulbs from the total of remaining 74 bulbs;


    . . . and so on 5 times, in all, completing your selection.



If you are familiar with the notion/conception of COMBINATIONS, you may write the formula for probability in this way


    P = ,


which says that the total space of events contains    elements,

while the space of favorable events has   elements.



Both formulas produce the same value and the same answer.


Your problem/question is solved,  answered,  explained and completed.


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To learn the subject better by examples,  look into the lessons
    - Elementary Probability problems related to combinations
    - Elementary Probability problems related to combinations REVISITED
in this site.

You will find a variety of similar  (and different)  solved problems there  (!)



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