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(#M40154014) MATHS Numerical Ability question probability Keep an EYE

There are 8 positive numbers and 6 negative numbers. 4 numbers are chosen at random and multiplied. Find the probability that the product is a positive number ?

Asked In Maths Neeraja (9 years ago)

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sheetal singh  (9 years ago)

Is it 505/1001?

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Mathe  (9 years ago)

Ways of choosing 4 numbers out of 14 given numbers (8 +ve and 6 -ve) = 14C4

Ways of choosing 4 numbers such that product is positive = 8C2*6C2 + 8C4 + 6C4
(choose 2 from 8 +ve and 2 from 6 -ve numbers + choose all from 8 +ve numbers + choose all from 6 -ve numbers)

Required Probability = Ways of choosing such that we get positive product / Total ways of choosing
Required Probability = 505/1001 = 0.504

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Chirag  (8 years ago)

It is 239/1001
Because, The total number of outcomes is 1001 - C(14,4)
For the result to be positive, you must choose-
1. 4 NEGATIVE NUMBERS
2. 2 NEGATIVE NUMBERS, Other 2 Positive numbers.
3. 4 POSITIVE NUMBERS
(1) can be done in C(4,4) ways. ie 1 Way
(2) 2 negative numbers can be chosen in C(4,2) ways and the other two positive numbers in C(8,2) ways.
Totally C(4,2)*C(8,2) ways
(3) 4 positive numbers can be chosen in C(8,4) ways.
(1),(2) and (3) are mutually exclusive.
C(4,4) + C(4,2)*C(8,2) + C(8,4) = Number of sample spaces
hence, evaluate and add, to get 239
The probability is 239/1001
Hope this helped!

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