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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 ?
- a)1001/505
- b)101/505
- c)505/1001
- d)450/965
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
There are 8 positive numbers and 6 negative numbers. 4 numbers are cho...
Explanation :
14C4 = 14*13*12*11/4*3*2*1 = 1001
4 No positive+4 no negative + (2 no positive * 2 no negative)
= 6C4 + 8C4 +(6C2 x8C2) = 15+70+15*28 = 505
P = 505/1001
Most Upvoted Answer
There are 8 positive numbers and 6 negative numbers. 4 numbers are cho...
Solution:
Given, there are 8 positive numbers and 6 negative numbers.
We need to find the probability that the product of 4 randomly chosen numbers is a positive number.
To find the probability, we need to find the number of ways in which the product of 4 randomly chosen numbers is positive and divide it by the total number of ways in which 4 numbers can be chosen from the given set of 14 numbers.
Let's first find the total number of ways in which 4 numbers can be chosen from the given set of 14 numbers.
Total number of ways = 14C4 = (14*13*12*11)/(4*3*2*1) = 1001
Now, let's find the number of ways in which the product of 4 randomly chosen numbers is positive.
Case 1: All 4 numbers are positive
Number of ways = 8C4 = (8*7*6*5)/(4*3*2*1) = 70
Case 2: 3 numbers are positive and 1 number is negative
Number of ways = (8C3)*(6C1) = (8*7*6/3*2*1)*6 = 336
Case 3: 2 numbers are positive and 2 numbers are negative
Number of ways = (8C2)*(6C2) = (8*7/2*1)*(6*5/2*1) = 420
Total number of ways in which the product of 4 randomly chosen numbers is positive = 70+336+420 = 826
Therefore, the probability that the product of 4 randomly chosen numbers is a positive number = (number of ways in which the product of 4 randomly chosen numbers is positive)/(total number of ways in which 4 numbers can be chosen from the given set of 14 numbers) = 826/1001 = 505/1001
Hence, the correct option is C) 505/1001.
Given, there are 8 positive numbers and 6 negative numbers.
We need to find the probability that the product of 4 randomly chosen numbers is a positive number.
To find the probability, we need to find the number of ways in which the product of 4 randomly chosen numbers is positive and divide it by the total number of ways in which 4 numbers can be chosen from the given set of 14 numbers.
Let's first find the total number of ways in which 4 numbers can be chosen from the given set of 14 numbers.
Total number of ways = 14C4 = (14*13*12*11)/(4*3*2*1) = 1001
Now, let's find the number of ways in which the product of 4 randomly chosen numbers is positive.
Case 1: All 4 numbers are positive
Number of ways = 8C4 = (8*7*6*5)/(4*3*2*1) = 70
Case 2: 3 numbers are positive and 1 number is negative
Number of ways = (8C3)*(6C1) = (8*7*6/3*2*1)*6 = 336
Case 3: 2 numbers are positive and 2 numbers are negative
Number of ways = (8C2)*(6C2) = (8*7/2*1)*(6*5/2*1) = 420
Total number of ways in which the product of 4 randomly chosen numbers is positive = 70+336+420 = 826
Therefore, the probability that the product of 4 randomly chosen numbers is a positive number = (number of ways in which the product of 4 randomly chosen numbers is positive)/(total number of ways in which 4 numbers can be chosen from the given set of 14 numbers) = 826/1001 = 505/1001
Hence, the correct option is C) 505/1001.
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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 ?a)1001/505b)101/505c)505/1001d)450/965Correct answer is option 'C'. Can you explain this answer?
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