# Moderate Probability Solved QuestionAptitude Discussion

 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

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:

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

$=\dfrac{15+70+15\times 28}{1001}$

$=\dfrac{505}{1001}$

Nithya
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