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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.

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.


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

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
            nCr = 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) = 15C­­­­­3…………………………..(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 4C2.
·         from Yellow + Green balls total = 5 + 6 = 11 only 1 ball is drawn i.e. n = 11, r = 1
It means 11C1.
Combine the Special cases which are discussed above as:
                        P (S) = 4C2 * 11C1 ……………………………(ii)
Then Probability P will become
                        P = P (S) / P (G)
                        Put these values from (i) & (ii), We get
                        P = 4C2 * 11C1 / 15C­­­­­3

Now                 4C2 = 4!/ 2!*(4-2)! = 6
                        11C1 = 11! / 1!*(11-1)! = 11
So                    P (S) = 4C2 * 11C1 / 15C­­­­­3 = 6 * 11 = 66
&                     P(G) = 15C­­­­­3 = 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) = 5C2 * 10C1
            P (S) = 10 * 10 = 100
&         P (G) = 15C­­­­­3 = 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.

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