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mathdad
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Can someone please explain the probability of replacement and without replacement with one simple example for each?
RTCNTC said:Can someone please explain the probability of replacement and without replacement with one simple example for each?
RTCNTC said:The ideas are not easy to grasp.
RTCNTC said:Probability word problems are tricky and require lots of practice. Wish I had more time on my hands.
MarkFL said:You would likely be better off getting your hands on a textbook dedicated to probability to learn the development of the elementary techniques. But, you are fortunate, there are several folks here who are quite knowledgeable in this topic and who can provide guidance if you delve into this area of study. (Yes)
RTCNTC said:Trust me, I will dive completely into a probability textbook in the coming months. Can you recommend a good probability textbook from amazon.com? Usually, it is not just probability alone. Most of the time, textbooks in this area of math include statistics.
MarkFL said:No, I don't have a good recommendation...I would try your local library first. :D
RTCNTC said:What about asking someone in this forum?
MarkFL said:Those who are both interested in probability and who may have a recommendation will likely read this thread. While I know several people here who know a great deal about probability, I don't want to name any names because that would place undue pressure on those members. It is best to let people volunteer information free from being "called out." :D
The textbook I used as a student was "Introductory Statistics, 3rd Edition" by Weiss/Hasset, ISBN 0-201-17833-8, Copyright 1991 by Addison-Wesley Publishing Co., Inc.
RTCNTC said:Since I am not going to dive deep into probability right now, I will search through amazon when the time is right. I want to continue posting from the David Cohen precalculus textbook, which has over 500 questions. Good night.
MarkFL said:Cohen might be a good source for problems, however, for development of the theory, there are likely much better texts dedicated to the topic...that's all I'm saying here. And you might find good texts at your local library, that you can read, gain a better understanding, then return, without putting out any cash. :D
Replacement in probability means that the item being selected is being put back into the pool of possible outcomes before each selection. Without replacement means that the item is not being put back and therefore the pool of possible outcomes is decreasing with each selection.
Replacement and without replacement can affect the probability of an event because with replacement, the pool of possible outcomes remains the same for each selection, while without replacement, the pool of possible outcomes decreases with each selection. This means that the probability of certain outcomes may be higher or lower depending on whether replacement or without replacement is used.
Replacement is more commonly used in real-world situations because it allows for a larger number of possible outcomes and therefore can more accurately reflect real-life scenarios. Without replacement is often used in situations where the number of possible outcomes is limited or when the pool of outcomes needs to decrease with each selection.
To calculate probability with replacement, you would use the formula P(A) = n(A)/n(S), where n(A) is the number of favorable outcomes and n(S) is the total number of possible outcomes. To calculate probability without replacement, you would use the formula P(A) = n(A)/n(S-n), where n(A) is the number of favorable outcomes and n(S-n) is the total number of possible outcomes after the previous selections have been made.
It would be more appropriate to use replacement in situations where the pool of possible outcomes needs to remain constant for each selection, such as in rolling a die multiple times. Without replacement would be more appropriate in situations where the pool of possible outcomes needs to decrease with each selection, such as in drawing cards from a deck without replacing them.