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MATH SHORT CUT TRICKS TO SOLVE PROBABILITY IN MATH- DOWNLOAD MATH TRICKS FOR PROBABILITY-100% RELIABLE ACCURATE & FASTEST METHOD TO SOLVE PROBABILITY- www.cutoffmarksresults.in

PROBABILITY
is important part of Mathematic in SSC IBPS or any other competitive exam
covers 2-5 questions used to check analytical skill of a candidate.

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**MATH SHORT CUT TRICKS TO SOLVE PROBABILITY**

Most
of the candidates get confused and choose wrong option of a question because of
superficial concept of PROBABILITY question. These are very easy and time
saving questions need to be solved within 2-3 seconds by ONE SIMPLE RULE.

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**ONE SIMPLE RULE FOR
PROBABILITY: **MATH SHORT CUT TRICKS TO SOLVE PROBABILITY

There
are two types of cases need to be discussed in the any PROBABILITY questions
which are based on selection of a number among a defined set of numbers.

Let P= Probability

S= Special Case

G= General Case

So P (S) = Probability of Special Case

P (G) = Probability of General Case

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**REMEMBER -ONE SIMPLE RULE: **MATH SHORT CUT TRICKS TO SOLVE PROBABILITY

** P
= P (S) / P (G)**

Use
Combination for making selection of numbers among a definite set of numbers.

Let C = Combination

n = Total numbers in a set

r = selected numbers among set of
numbers

Then

^{n}C_{r }^{= }n!
/ r! (n-r)!

Where !
= Factorial of a number (see example for
clarity)

Note:
For ‘AND’ = Use Addition of Probability & for ‘OR’ = Use Multiplication of
Probability

**Question
1: **

A bag
contains 4 Red and 5 Yellow & 6 Green balls. 3 balls are drawn (selected) at
random.

a.
What
is the probability that balls are drawn contains exactly two Red.

b.
What
is the probability that balls are drawn contains exactly two Yellow.

**Solution:**

In
this question:

Colors-----à Red Yellow Green TOTAL
(Set of Numbers = n)

Balls------à 4 5 6 15

Read
the statement and find the General Condition in question. In above question,
the general condition is to draw 3 balls randomly which implies Probability of
General Case i.e. n = 15, r = 3. So

P (G) = ^{15}C_{3}…………………………..(i)

Now
discuss the special cases P (S) as follows:

**a.
****What is the probability that
balls are drawn contains exactly two Red.**

In the above case 3 balls are
drawn in which exactly 2 balls are drawn from Red and 1 ball is drawn except
Red balls (i.e. Yellow + Green balls = 5 + 6 = 11) that means

·
from
set of Red balls total = 4 exactly 2 ball are drawn i.e. n = 4, r = 2

It
means ^{4}C_{2}.

·
from
Yellow + Green balls total = 5 + 6 = 11 only 1 ball is drawn i.e. n = 11, r = 1

It
means ^{11}C_{1}.

Combine
the Special cases which are discussed above as:

P (S) = ^{4}C_{2
}* ^{11}C_{1 }……………………………(ii)

Then
Probability P will become

** P = P (S) / P (G)**

** **Put these values from (i) &
(ii), We get

** P
= **^{4}C_{2 }* ^{11}C_{1
}/ ^{15}C_{3}

Now ^{4}C_{2 }= 4!/
2!*(4-2)! = 6

^{11}C_{1}
= 11! / 1!*(11-1)! = 11

So **P (S) = **^{4}C_{2 }* ^{11}C_{1 }/ ^{15}C_{3}
= 6 * 11 = 66

& P(G) = ^{15}C_{3
}= 15! / 3! * (15-3)! = 455

Thus **P = P (S) / P (G) = 66 / 455 Ans.**

**b.
****What is the probability that
balls are drawn contains exactly two Yellow.**

P (S) = ^{5}C_{2 }*
^{10}C_{1}

P (S) = 10 * 10 = 100

& P (G) = ^{15}C_{3 }=
15! / 3! * (15-3)! = 455

Thus **P = P (S) / P (G) = 100 / 455 Ans.**

Do the
practice of such questions by using ONE SIMPLE RULE Method from any set of
previous question papers and score cut-off marks in SSC IBPS or other
competitive exams.