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Hi GMATters,
In this new blog post (with pictures)! I show you how to derive the basic GMAT Probability equations: when you multiply, when you add, how to see whether a circumstance is Mutually Exclusive.
https://privategmattutor.london/the-bas ... ort-guide/
Read an excerpt here:
The Basic GMAT Probability Equations
First, we need to establish some sort of general definition for the term Probability itself. You’ll most often hear Probability defined as some variant of:
desired outcomes / total outcomes
First things first: Probability is always a fraction, which, of course, could also be a percent (because these two statements, at the end of the day, mean the same thing).
Second: if all of the all the desired outcomes are represented by all the total outcomes, then you have a fraction equal to 1 (or 100%).
Let’s say you want a black kitten and your neighbor’s cat just had a litter, then the Probability of getting a black kitten is the number of black kittens divided by the number of total kittens in the litter.
If we go to visit and all four kittens in the litter are black, then your Probability of getting a black kitten is:
4/4 = 1
In other words, you will invariably select a black kitten because all of the kittens are black.
That said, saying you have a 100% chance of anything is a trivial statement simply because (in most cases) this will be obvious.
In other words, the statement contains no useful information. I mean if all the cats are black, then whichever you select will be black, yes?
Probability works better, of course, when your desired outcomes are fewer than your total outcomes.
Now let’s look at the GMAT Probability equations that you’re most likely to see.
Basic GMAT Probability Equations
This is better learned through example.
Let’s start by imagining a normal deck of cards. That of course means 52 cards: four suits and 13 cards per suit. No jokers.
Now–for those of you who aren’t Mötörhead fans–what is the probability that, selecting one card at random from this deck, you pull the Ace of Spades?
Well, consider how many cards there are: 52. In other words, find the total outcomes, which will generally be fairly straightforward.
It makes a nice first step–nice to know that at least we’ve accomplished one thing so far!
Now we need to consider the number of desired outcomes: in this case, it’s the Ace of Spades, of which there is only one.
That is, we find that the Probability of pulling the Ace of Spades is:
1/52
Hopefully this is straightforward so far, because we need to build off the fact that it’s self-evident that we find only one Ace of Spades within the deck.
Following the same thinking, we should find four Aces in total. That means that the probability of pulling an Ace (of any suit) is:
P(A)= 4/52 = 1/13
Likewise, pulling a Spade (of any face or number) is:
P(S) = 13/52 = 1/4
Here’s the clever part: notice that 1 × 1 = 1 . In other words–using ⋀to mean “and”–we can say that...
Read the rest here: The Basic GMAT Probability Equations
First, we need to establish some sort of general definition for the term Probability itself. You’ll most often hear Probability defined as some variant of:
desired outcomes / total outcomes
First things first: Probability is always a fraction, which, of course, could also be a percent (because these two statements, at the end of the day, mean the same thing).
Second: if all of the all the desired outcomes are represented by all the total outcomes, then you have a fraction equal to 1 (or 100%).
Let’s say you want a black kitten and your neighbor’s cat just had a litter, then the Probability of getting a black kitten is the number of black kittens divided by the number of total kittens in the litter.
If we go to visit and all four kittens in the litter are black, then your Probability of getting a black kitten is:
4/4 = 1
In other words, you will invariably select a black kitten because all of the kittens are black.
That said, saying you have a 100% chance of anything is a trivial statement simply because (in most cases) this will be obvious.
In other words, the statement contains no useful information. I mean if all the cats are black, then whichever you select will be black, yes?
Probability works better, of course, when your desired outcomes are fewer than your total outcomes.
Now let’s look at the GMAT Probability equations that you’re most likely to see.
Basic GMAT Probability Equations
This is better learned through example.
Let’s start by imagining a normal deck of cards. That of course means 52 cards: four suits and 13 cards per suit. No jokers.
Now–for those of you who aren’t Mötörhead fans–what is the probability that, selecting one card at random from this deck, you pull the Ace of Spades?
Well, consider how many cards there are: 52. In other words, find the total outcomes, which will generally be fairly straightforward.
It makes a nice first step–nice to know that at least we’ve accomplished one thing so far!
Now we need to consider the number of desired outcomes: in this case, it’s the Ace of Spades, of which there is only one.
That is, we find that the Probability of pulling the Ace of Spades is:
1/52
Hopefully this is straightforward so far, because we need to build off the fact that it’s self-evident that we find only one Ace of Spades within the deck.
Following the same thinking, we should find four Aces in total. That means that the probability of pulling an Ace (of any suit) is:
P(A)= 4/52 = 1/13
Likewise, pulling a Spade (of any face or number) is:
P(S) = 13/52 = 1/4
Here’s the clever part: notice that 1 × 1 = 1 . In other words–using ⋀to mean “and”–we can say that...
Read the rest here: https://privategmattutor.london/the-bas ... ort-guide/
In this new blog post (with pictures)! I show you how to derive the basic GMAT Probability equations: when you multiply, when you add, how to see whether a circumstance is Mutually Exclusive.
https://privategmattutor.london/the-bas ... ort-guide/
Read an excerpt here:
The Basic GMAT Probability Equations
First, we need to establish some sort of general definition for the term Probability itself. You’ll most often hear Probability defined as some variant of:
desired outcomes / total outcomes
First things first: Probability is always a fraction, which, of course, could also be a percent (because these two statements, at the end of the day, mean the same thing).
Second: if all of the all the desired outcomes are represented by all the total outcomes, then you have a fraction equal to 1 (or 100%).
Let’s say you want a black kitten and your neighbor’s cat just had a litter, then the Probability of getting a black kitten is the number of black kittens divided by the number of total kittens in the litter.
If we go to visit and all four kittens in the litter are black, then your Probability of getting a black kitten is:
4/4 = 1
In other words, you will invariably select a black kitten because all of the kittens are black.
That said, saying you have a 100% chance of anything is a trivial statement simply because (in most cases) this will be obvious.
In other words, the statement contains no useful information. I mean if all the cats are black, then whichever you select will be black, yes?
Probability works better, of course, when your desired outcomes are fewer than your total outcomes.
Now let’s look at the GMAT Probability equations that you’re most likely to see.
Basic GMAT Probability Equations
This is better learned through example.
Let’s start by imagining a normal deck of cards. That of course means 52 cards: four suits and 13 cards per suit. No jokers.
Now–for those of you who aren’t Mötörhead fans–what is the probability that, selecting one card at random from this deck, you pull the Ace of Spades?
Well, consider how many cards there are: 52. In other words, find the total outcomes, which will generally be fairly straightforward.
It makes a nice first step–nice to know that at least we’ve accomplished one thing so far!
Now we need to consider the number of desired outcomes: in this case, it’s the Ace of Spades, of which there is only one.
That is, we find that the Probability of pulling the Ace of Spades is:
1/52
Hopefully this is straightforward so far, because we need to build off the fact that it’s self-evident that we find only one Ace of Spades within the deck.
Following the same thinking, we should find four Aces in total. That means that the probability of pulling an Ace (of any suit) is:
P(A)= 4/52 = 1/13
Likewise, pulling a Spade (of any face or number) is:
P(S) = 13/52 = 1/4
Here’s the clever part: notice that 1 × 1 = 1 . In other words–using ⋀to mean “and”–we can say that...
Read the rest here: The Basic GMAT Probability Equations
First, we need to establish some sort of general definition for the term Probability itself. You’ll most often hear Probability defined as some variant of:
desired outcomes / total outcomes
First things first: Probability is always a fraction, which, of course, could also be a percent (because these two statements, at the end of the day, mean the same thing).
Second: if all of the all the desired outcomes are represented by all the total outcomes, then you have a fraction equal to 1 (or 100%).
Let’s say you want a black kitten and your neighbor’s cat just had a litter, then the Probability of getting a black kitten is the number of black kittens divided by the number of total kittens in the litter.
If we go to visit and all four kittens in the litter are black, then your Probability of getting a black kitten is:
4/4 = 1
In other words, you will invariably select a black kitten because all of the kittens are black.
That said, saying you have a 100% chance of anything is a trivial statement simply because (in most cases) this will be obvious.
In other words, the statement contains no useful information. I mean if all the cats are black, then whichever you select will be black, yes?
Probability works better, of course, when your desired outcomes are fewer than your total outcomes.
Now let’s look at the GMAT Probability equations that you’re most likely to see.
Basic GMAT Probability Equations
This is better learned through example.
Let’s start by imagining a normal deck of cards. That of course means 52 cards: four suits and 13 cards per suit. No jokers.
Now–for those of you who aren’t Mötörhead fans–what is the probability that, selecting one card at random from this deck, you pull the Ace of Spades?
Well, consider how many cards there are: 52. In other words, find the total outcomes, which will generally be fairly straightforward.
It makes a nice first step–nice to know that at least we’ve accomplished one thing so far!
Now we need to consider the number of desired outcomes: in this case, it’s the Ace of Spades, of which there is only one.
That is, we find that the Probability of pulling the Ace of Spades is:
1/52
Hopefully this is straightforward so far, because we need to build off the fact that it’s self-evident that we find only one Ace of Spades within the deck.
Following the same thinking, we should find four Aces in total. That means that the probability of pulling an Ace (of any suit) is:
P(A)= 4/52 = 1/13
Likewise, pulling a Spade (of any face or number) is:
P(S) = 13/52 = 1/4
Here’s the clever part: notice that 1 × 1 = 1 . In other words–using ⋀to mean “and”–we can say that...
Read the rest here: https://privategmattutor.london/the-bas ... ort-guide/
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