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31 May 2008, 04:30
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1. A box contains 100 balls each numbered 1 to 100. 3 balls are picked in random with replacement - what is the probability that the sum is Odd?
1. 1/4
2. 3/8
3. 1/2
4. 5/8
5. 3/4
OA= 1/2
How can this be right?? The solution has ignored one possiblity where in case of Odd, Even, Even (all 3 ways) when both the even numbers are the same - this makes a double count what say?
Same is the case with Odd, odd, odd combo!
1. 1/4
2. 3/8
3. 1/2
4. 5/8
5. 3/4
OA= 1/2
How can this be right?? The solution has ignored one possiblity where in case of Odd, Even, Even (all 3 ways) when both the even numbers are the same - this makes a double count what say?
Same is the case with Odd, odd, odd combo!
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31 May 2008, 05:06
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Answer Has to be 1/2.
Explanation 1: There is equal number of odd number and equal number of even number. As there is no bias to any of them, so chances of obtaining sum of odd or sum of even has to be equally likely events and hence they will each have probability = 1/2.
Explanation 2:
Odd sum can be obtained in 2 ways = odd + odd + odd or Even + Even + Odd
Number of even numbers = 50
Number of odd numbers = 50
Probability = 50c3/100c3 + 50c2*50c1/100c3 = 1/2
Explanation 1: There is equal number of odd number and equal number of even number. As there is no bias to any of them, so chances of obtaining sum of odd or sum of even has to be equally likely events and hence they will each have probability = 1/2.
Explanation 2:
Odd sum can be obtained in 2 ways = odd + odd + odd or Even + Even + Odd
Number of even numbers = 50
Number of odd numbers = 50
Probability = 50c3/100c3 + 50c2*50c1/100c3 = 1/2
31 May 2008, 12:25
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To produce odd addition:
odd + even + even => P = 1/2 * 1/2 * 1/2 = 1/8
even + odd + even => P = 1/8
even + even + odd => P = 1/8
odd + odd + odd => P = 1/8
1/8 * 4 = 1/2
odd + even + even => P = 1/2 * 1/2 * 1/2 = 1/8
even + odd + even => P = 1/8
even + even + odd => P = 1/8
odd + odd + odd => P = 1/8
1/8 * 4 = 1/2
