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 ?

• Is it 505/1001?
• 8 years agoHelpfull: Yes(0) No(1)
• 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
• 8 years agoHelpfull: Yes(0) No(0)
• 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!
• 8 years agoHelpfull: Yes(0) No(0)