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08 May 2026, 21:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
25% (05:10) correct
75%
(01:26)
wrong
based on 4
sessions
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If three distinct positive integers from 1 to n are chosen at random, the probability that the product of the first two integers is odd is 2/9. What is the probability that the product of the all three integers is odd?
A. 1/18
B. 1/15
C. 2/27
D. 1/12
E. 1/9
A. 1/18
B. 1/15
C. 2/27
D. 1/12
E. 1/9
09 May 2026, 00:41
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Here’s how I approached it mentally.
For the product of the first two integers to be odd, both numbers must be odd.
So if the probability is given as:
2/9
I tried expressing it in the form:
(O/N) × ((O−1)/(N−1))
where:
O = number of odd integers
N = total integers
Now I looked for values that fit 2/9 naturally.
Trying:
10 × 9 = 90
So the numerator should become:
2 × 10 = 20
And 20 can be written as:
5 × 4
That matches perfectly with:
(O/N) × ((O−1)/(N−1))
= (5/10) × (4/9)
= 20/90
= 2/9
So there are 5 odd numbers out of 10 total numbers.
Now for the product of all three integers to be odd, the third number must also be odd.
After choosing two odd numbers, we have:
3 odd numbers left out of 8 remaining numbers.
So:
P(all three product odd)
= (2/9) × (3/8)
= 6/72
= 1/12
Answer: D
I found it faster to reverse-engineer the fraction first instead of setting up equations directly.
— Rajdeep
For the product of the first two integers to be odd, both numbers must be odd.
So if the probability is given as:
2/9
I tried expressing it in the form:
(O/N) × ((O−1)/(N−1))
where:
O = number of odd integers
N = total integers
Now I looked for values that fit 2/9 naturally.
Trying:
10 × 9 = 90
So the numerator should become:
2 × 10 = 20
And 20 can be written as:
5 × 4
That matches perfectly with:
(O/N) × ((O−1)/(N−1))
= (5/10) × (4/9)
= 20/90
= 2/9
So there are 5 odd numbers out of 10 total numbers.
Now for the product of all three integers to be odd, the third number must also be odd.
After choosing two odd numbers, we have:
3 odd numbers left out of 8 remaining numbers.
So:
P(all three product odd)
= (2/9) × (3/8)
= 6/72
= 1/12
Answer: D
I found it faster to reverse-engineer the fraction first instead of setting up equations directly.
— Rajdeep
