Mathematics is a wonderful subject and has its vocabulary and uses many English words like AND, OR, Equal to, Union, and nor, to name a few.
AND & OR are the two most confusing aspects for many students because they don’t understand whether they mean addition or multiplication.
The problem increases when we study these keywords in the probability chapter, where both these become critical.
We must understand one thing that these both are operations and not simply the signs like multiplying or dividing.
What Does AND Mean in Math?
In probability, the distinction is clear, and in simple math logic symbol, + means AND.
- AND needs both conditions to be true to be valid; true means satisfying the conditions.
- OR is mostly okay with anyone or both the conditions getting true for it takes place.
Understanding the AND & OR probabilities:
By now, we understand that AND refers to the outcome must satisfy both the given conditions at once and OR mean any one or two or all.
- For instance, what is the probability of if we take out a card from its deck and it must be red AND face card?
- As per the meaning of the term AND, we need to look at the joint probability of such a card which satisfies both conditions of the outcome from this sample.
- There are only six possible cards here which Jack, Queen, and a King of Hearts and diamonds.
- Using formula, P = 6/52 = 11.5% approx.
- Now, what if the same question asked to take out a card that has Red OR a face card?
- Now, the meaning has changed completely.
- We can pick any card, whether it’s red, a face card, or both red and a face.
- This gives us twenty-six cards in total, which are red, which already include the face card in themselves, and six cards as both.
- We now have thirty-two such cards, which give us P = 32/ 52; deck has fifty-two cards in total, = 61.5% approx.
- See how changing just one word AND to OR changed the answer by so much.
PS – In the OR problem, we do not add twelve face cards to twenty-six red cards because we already have six face cards that are red as well.
If one is not careful, he will get 38 cards instead of 32.
Most common mathematical symbols and notations:
+ This symbol is read as PLUS, and it is an addition sign, logically means AND.
* This symbol means multiplication, logically means OR.
X Multiplication or times and product of the values.
. Dot product, X cross product.
! Factorial, do the product of all the positive integers.
Some recommended items:
01. Probability: For the Enthusiastic Beginner – $6.75 – Kindle and $20.09 for Paperback – By David Morin
- Book will serve as a great inspiration to high-school students and college who are first-time beginning their learning phase.
- Some of the major topics are Bayes theorem, central limit, regression, correlation, and prob. Density.
02. Bayesian Statistics the Fun Way – $16.76 – Kindle and $29.99 for Paperback – By WILL
- The book emphasizes the importance of probability and stats in many professions, but many don’t understand it properly.
- It explains everything in a friendly manner with lots of examples that settle in our brains.
Some other questions,
Related Questions and Frequently Asked Questions (FAQ):
Q1.) Can we say that and mean to multiply the terms?
Answer: No!
If the mathematical actions are independent, then the action taking place on one of them cannot affect the other.
So, and means multiply just a lighter satire in probability.
Q2.) Does and sign signify multiplication or addition?
Answer: Whenever an individual applies an OR operation, they join all the given result sets, which seems as you are adding them.
Grouping and adding are different.
Rather than seeing them as multiplication or addition, we recommend you see them as operations on the given result set.
Q3.) What does the decimal sign indicate in multiplication?
Answer: We understand you are referring to this problem here, X.Y, where we multiply both terms.
The real reason is to avoid confusion in those algebraic terms which already have an X attached with them.
For instance, X.Y is less confusing than X x Y, though both mean the same.
Q4.) Can we replace equal to sign with or?
Answer: No, both are different. = and or are not the same.
The confusion occurs because, in some of the daily routines, an anomaly appears that confuses us often.
But when it comes to LOGIC, they both are different; that’s why we call or as a logical operators.
Q5.) Does AND mean to multiply the terms in probability?
Answer: Interestingly, No!
It happens because, in probability language, we often translate the word OR into addition, AND as an addition.
However, there are two assumptions behind them which no one studies that only to add the events if they are disjoint and multiply them if independent.
Q6.) What does AND & OR mean in probability?
Answer: There is a clear distinction between both the words, where AND refers to that outcome which can satisfy and two conditions but at the same time.
On the other hand, OR means it must satisfy either of the two conditions or both.
Q7.) What does the Inverted V symbol mean?
Answer: ∧Wedge!
Wedge is the symbol for mathematics logic and is an important Boolean function operator.
It means that if we have two arguments, then it comes true if all the other arguments also prove to be true.
Q8.) What does not equal to mean in math?
Answer: ≠, This means as its name suggests, that the logic on its two sides is not accurate enough.
For instance, 11-4 ≠ 4-11.
Q9.) Does AND symbol shows any decimal?
Answer: if we write a number, AND can denote the decimal for sure, and congratulations, you have a myth!
For instance, If I say twenty-five times five is one hundred AND twenty-five, I mean 125 and not 1.25 or 12.5 at all!
Q10.) How to calculate PA and B?
Answer: P (A and B) = Pa. Pb because A and B were independent events, and one probability even can never affect the other, so simply multiply them.
Q11.) Is it a UNION, AND, or OR?
Answer: A Union, U occurs when an element occurs in two sets such that it is present in the first, the second, and in both. OR words also describe them.
Q12.) What are PA and PB?
Answer: We can call them the conditional probability of event A occurs, and due to that, event B also triggers or vice-versa.
Joint probability if both will happen together or both are occurring.
Q13.) What is one key difference between both AND OR?
Answer: Simple!
Or needs to satisfy any of the inequalities or both.
AND needs to mandatorily satisfy both.
Q14.) What is the meaning of twice in math?
Answer: 2x, where x is any number.
Double or multiply any number with two in simple words.
For instance, twice of four is eight.
Twice of 2.5 is five., Twice of 5Y is 10Y.
Similarly, thrice means three times or multiplying any number with three. Like thrice of 20 = 60, thrice of three = nine, and thrice of 40X = 120X.
Q15.) What is BODMAS?
Answer: It is a clever and simple mathematical rule that lets you solve mathematical operations in only that order.
Where B- Bracket, O- Orders, D- Division, M-Multiplication, A-Addition, S-Subtraction.
Bracket first solve big, then curly, then round and order means powers or root indices.
Q16.) Can we consider Pi as a real number?
Answer: Yes!
Pi is an irrational and real number that one cannot express by simple fractions.
Most students get its introduction from the basic numerical value this number possesses, like 22/7 or 3.14.
Q17.) What does an arrow sign indicate in the geometry?
Answer: They show parallel lines.
Cross shows intersection.
Q18.) What does Y indicate in the mathematical numbers?
Answer: In coordinated geometry, this Y shows the value of the vertical coordinate pair.
This value has its notation after the X value only, which is the horizontal axis.
X, Y.
12, 8 means Y = 8.
Final Verdict:
Mathematics uses a beautiful language that has its own set of expressions, notations, and symbols.
AND symbols are a logical operation like OR. Both also have a great application in probability and statistics.
In the language of probability, AND means when the outcome must satisfy two of the given conditions properly, only then will it come under the true logic.
On the other hand, OR means the outcome can satisfy anyone condition or the other or both of them.
For instance, if you want both Red AND face cards from a deck of cards, you will only get six such cards which will be the K, Q, and J of Diamond and heart.
Similarly, if in the same question we say red OR face cards, we can get around thirty-two cards for the same logical set.
This is because we will include all the twenty-six red cards, and both red and face cards as six, and no face card again as they will come double otherwise.
So, by just changing a single word, we managed to change so much.
Thanks For Reading!