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# Probability Example

Shortcut tricks on probability are one of the most important topics in exams. Time takes a huge part in competitive exams. If you manage your time then you can do well in those exams. Most of us miss that part. Few Probability example shortcuts is given in this page below. All tricks on probability are provided here. Visitors please read carefully all shortcut examples. These examples will help you to understand shortcut tricks on Probability.

First of all do a practice set on math of any exam. Write down twenty math problems related to this topic on a page. Solve first ten math problems according to basic math formula. You also need to keep track of Timing. Write down the time taken by you to solve those questions. Now read our examples on probability shortcut tricks and practice few questions. After doing this go back to the remaining ten questions and solve those using shortcut methods. Again keep track of the time. You will surely see the improvement in your timing this time. But this is not all you want. You need to practice more to improve your timing more.

### Few Important things to Remember

We all know that the most important thing in competitive exams is Mathematics. That doesn’t mean that other topics are less important. You can get a good score only if you get a good score in math section. A good score comes with practice and practice. The only thing you need to do is to do your math problems correctly and within time, and you can do this only by using shortcut tricks. But it doesn’t mean that without using shortcut tricks you can’t do any math problems. You may do math problems within time without using any shortcut tricks. You may have that potential.

But, so many people can’t do this. So Probability shortcut tricks here for those people. Here in this page we try to put all types of shortcut tricks on Probability. But we may miss few of them. If you know anything else rather than this please do share with us. Your little help will help so many needy.

### Probability Example #1

Suman enter in a food mall to buy marshmallow, kitkat and donuts. He has to purchase at least 9 unit of each. He purchase more kitkat than marshmallow and more donuts than kitkat. And, he picked up a total 32 items. Find the number of kitkat he purchased.

1. 9 or 10
2. 10 or 11
3. 11 or 12
4. 12 or 13

Show Answer Show How to Solve Open Rough Workspace

How to Solve
We know from the question,
Donuts > Kitkat > Marshmallow
So,
Either it’s 13>10>9
Or, 12>11>9

So, either 10 or 11.

Rough Workspace

### Probability Example #2

What is the probability of getting a sum 9 from two dice?

1. 1 / 5
2. 5 / 7
3. 1 / 9
4. 9 / 11

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How to Solve
In two dice,
n(S) = ( 6 x 6 )
= 36.

Let, E = event of getting a sum 9
= {( 4, 5 ), ( 5, 4 ), ( 6, 3 ), ( 3, 6 )}.

So, p(E) = n(E) / n(S)
then, 4 / 36
therefore, 1 / 9.

Rough Workspace

### Probability Example #3

Two dice are tossed. What is the probability that the total score is a prime number?

1. 5 / 12
2. 7 / 12
3. 9 / 12
4. 11 / 12

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How to Solve
We know that,
If two dice tossed, then n(S) = ( 6 x 6 ) = 36.

Let, E = Event that the sum is prime number,
So, E = { ( 1, 1 ), ( 1, 2 ), ( 1, 4 ), ( 1, 6 ), ( 2, 1 ), ( 2, 3 ), ( 2, 5 ), ( 3, 2 ), ( 3, 4 ), ( 4, 1 ), ( 4, 3 ), ( 5, 2 ), ( 5, 6 ), ( 6, 1 ), ( 6, 5 ) }
n(E) = 15.

So, p(E) = n(E) / n(S)
= 15 / 36
= 5 / 12.

Rough Workspace

### Probability Example #4

In a single throws of a die, what is probability of getting a number greater than 4?

1. 1 / 3
2. 2 / 3
3. 3 / 3
4. 1 / 6

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How to Solve
We throws of a die, so we have,
S{ 1, 2, 3, 4, 5, 6 }.

Let, E = Event of getting a number greater than 4 = { 5, 6 }.

So, P(E) = n(E) / n(S)
= 2 / 6
= 1 / 3.

Rough Workspace

### Probability Example #5

A number X is chosen at random from the numbers -5, -2, -1, 0, 1, 2, 5. What is the probability that (mod X<2)?

1. 2 / 7
2. 3 / 7
3. 4 / 7
4. 5 / 7

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How to Solve
X can take 7 values which is the total cases.
To get (mod X<2) here we assume as -2<X<+2,
So, we take X = (-1, 0, 1)
Now, P(mod X<2) = Favorable Cases / Total Cases
= 3 / 7.
Rough Workspace

### Few examples of Probability with Shortcut Tricks

1. 