The Addition Rule of Probability | Probability Theory, Sum Rule of Probability
What is the addition rule of probabiltiy? Also sometimes called the sum rule of probability, this rule tells us how to calculate the probability of the union of two events. In today’s math video lesson, we’ll explain the addition rule of probabiltiy for two events that are mutually exclsuive and for the general case when we don’t know if the events are mutually exclusive! We’ll also go over two examples of addition rule problems. It’s called the addition rule because, of course, it involved adding probabilties!
If A and B are two mutually exclusive events, then P(A U B) = P(A) + P(B). This is the addition rule for mutually exclusive events!
But what if we don’t know if two events are mutually exclusive? Or what if we know they are certainly not mutually exclusive? Then we can use this formula instead: P(A U B) = P(A) + P(B) - P(A intersect B). This comes from the fact that counting P(A) also includes P(A intersect B) by definition. However, when we add P(B), we are counting P(A intersect B) a second time, so we need to subtract P(A intersect B) in order to correct that double counting of the intersection! When two events are mutually exclusive, the probability of their intersection is 0, so we’d just be left with the original formula for the probability of the union of two mutually exclusive events.
Remember that mutually exclusive events are events that cannot occur simultaneously!
SOLUTION TO PRACTICE PROBLEM:
We are asked to find the probability of a randomly drawn card from a standard 52-card deck being red or an ace. We are considering two events.
A: The card is red
B: The card is an ace
A and B are not mutually exclusive because a card can be red and an ace (ace of hearts or ace of diamonds). We know, by the addition rule, P(A U B) = P(A) + P(B) - P(A intersect B). What is P(A)? There are 26 red cards and 52 cards total, so P(A) = 26/52. What is P(B)? There are four aces so P(B) = 4/52. What is P(A intersect B)? There are two red aces, so P(A intersect B) = 2/52. Thus, P(A U B) = 26/52 + 4/52 - 2/52 = 28/52.
If you are preparing for Probability Theory or in the midst of learning Probability Theory, you might be interested in the textbook I used in my Probability Theory course, called "A First Course in Probability Theory" by Sheldon Ross. Check out the book and see if it suits your needs! You can purchase the textbook using the affiliate link below which costs you nothing extra and helps support Wrath of Math!
PURCHASE THE BOOK: amzn.to/31mXEjr
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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Пікірлер: 46
clear and concise video, good job bud
I love how clear your voice is,plus thanks for breaking down this topic❤
@WrathofMath
Жыл бұрын
Thank you for watching!
🎉 thanks a million!
Thank you so much for clear explanation 😊❤
@WrathofMath
6 ай бұрын
My pleasure 😊
Reallyhelpful and well explained
@WrathofMath
2 жыл бұрын
Thanks a lot, I am glad it helped!
You're the best. Just subscribed
@WrathofMath
Жыл бұрын
Thank you!
How does one determine that the ace is red. given that we have two options.
such a great video
@WrathofMath
Жыл бұрын
Thank you!
Excellent explaination
@WrathofMath
3 ай бұрын
Glad it was helpful!
This was very helpful!
@WrathofMath
4 жыл бұрын
Glad to hear it! Thanks a lot for watching!
@Anand.5464
3 жыл бұрын
Bakwas hai
how do we know there are two 4 and 2 red aces. Please can you explain properly
thank u sir please make the video on total proability therom with example problems sir
@WrathofMath
3 жыл бұрын
Thanks for watching and here is my lesson on total probability: kzread.info/dash/bejne/h2eTmZpsqN3Ugaw.html I'll try to do a lesson with some more examples of applying it soon!
@teja4b132
3 жыл бұрын
@@WrathofMath thank you sir
Nice explanation brother thank u,subscribe
How to find again the (A intersect B)?
@WrathofMath
2 жыл бұрын
Thanks for watching! A intersect B is the set of all things common to both A and B. In terms of probability, A intersect B is "A and B". So if A = Rolling an even number and B = Rolling a prime number, then A intersect B is rolling an even and prime number, so the only outcome in that event would be rolling a 2.
Where did that two came from ...in the last question
Fun!
@WrathofMath
2 жыл бұрын
Agreed!
Since 1 is a prime number, shouldn't the set of numbers for a dice roll that is prime be 1, 2, 3, and 5?
@WrathofMath
Жыл бұрын
1 is not prime - a prime number is a positive integer with exactly 2 factors! But 1 only has one factor.
@carolmcsween-brooks9519
Жыл бұрын
@@WrathofMath Thank you so much! Wow! In the 1950's and 60's I was taught that 1 was a prime number and if I'm not mistaken this was taught right through to my college calculus. Not sure why the teaching wasn't in agreement with the current mathematicians. Now that I'm working with data science this is a significant revelation - for me though it's sort of like being told that Pluto is no longer a "planet." :D From my perspective, I could still see how one could be considered prime - its second factor is itself. But the key is that the factors of a prime number have to be two DIFFERENT numbers. So, thanks again. Your explanation of the addition rule of probability is great. 🙂
HII THANK YOU FOR THE USEFUL TEACHING PLEASE MAKE A VIDEO ON BAYES THEOREM
@WrathofMath
3 жыл бұрын
You're very welcome and thanks for watching! I'd be happy to make a video on Baye's Theorem, I'll try to do one soon! Thanks for the request!
@WrathofMath
3 жыл бұрын
Here it is! kzread.info/dash/bejne/Zad-0Jdmc83TYtY.html
@Anand.5464
3 жыл бұрын
You amrican
Water (splash). Really get splashy 💦
@WrathofMath
3 жыл бұрын
splishy splashy wrathy mathy
@pierrefernandes1870
3 жыл бұрын
Wrath of Math I’m lookin at my opp boy vids... and all I see is cali
Last question solution: 26/52 + 4/52 - 2/52 = 28/52 Is this Right?
@WrathofMath
4 жыл бұрын
Thanks for watching and great work, that's precisely right!
@loll1165
5 ай бұрын
This might sound silly, but where do you get the 26 from like how do you know its 26 out of 52
@Itachi_Zoldyck
5 ай бұрын
@loll1165 you add the diamond and the heart since they are red so diamond got 13 out of 52 and heart got 13 out of 52😅 finally 13+13=26. (26/52)👍
He is the messiah