Probability
Aptitude

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Q.

There are 6 positive and 8 negative numbers. Four numbers are chosen at random and multiplied. The probability that the product is a positive number is:

 A.

500/1001

 B.

503/1001

 C.

505/1001

 D.

101/1001

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Solution:
Option(C) is correct

The product of four numbers will be positive in the following ways.

All the four numbers are positive, hence probability:

\(=\dfrac{^6C_4}{^{14}C_4}\)

All the four numbers are negative, hence probability:

\(=\dfrac{^8C_4}{^{14}C_4}\)

Two numbers are positive and two are negative, hence Probability:

\(=\dfrac{^6C_2\times ^8C_2}{^{14}C_4}\)

Hence, required probability of the event: 

\(=\dfrac{^6C_4+^8C_4+(^6C_2\times ^8C_2)}{^{14}C_4}\)

\(=\dfrac{15+70+15\times 28}{1001}\)

\(=\dfrac{505}{1001}\)


(3) Comment(s)


Nithya
 ()

sir,answer will be 495/1001.



Poonam Pipaliya
 ()

sir it is not in options but we can also add the way 6C1*8C3 or 6C3*8C1 iwith 505,,,,aren't we...??..!!


Deepak
 ()

I am not able to understand your point, it would be nice if you elaborate more.