# 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:

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

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

$=\dfrac{505}{1001}$

## (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.