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01 Aug 2022, 17:15
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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:
55%
(hard)
Question Stats:
67% (02:10) correct
33%
(02:21)
wrong
based on 297
sessions
History
Date
Time
Result
Not Attempted Yet
{2, 3, 4, 5, 6}
If two numbers are selected at random one after the other, without replacement, from the list above, what is the probability that their product is divisible by 4?
A. 11/30
B. 2/5
C. 12/25
D. 1/2
E. 13/25
If two numbers are selected at random one after the other, without replacement, from the list above, what is the probability that their product is divisible by 4?
A. 11/30
B. 2/5
C. 12/25
D. 1/2
E. 13/25
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08 Aug 2022, 04:41
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If 4 is selected with any of the other 4 numbers, the product of the two numbers will be divisible by 4.
Also, as 4 can be selected in either of the attempts, the Total ways of the combination = 2*4 = 8
Also, if 2 and 6 are selected together, the product will be divisible by 4. This can be done in 2 ways.
Thus, total number of ways = 8 + 2 = 10.
The number of ways of selecting two numbers out of the 5 one after the other is 5*4 = 20
Thus, the required probability = 10/20 = 1/2.
Thus, the correct option is D.
Also, as 4 can be selected in either of the attempts, the Total ways of the combination = 2*4 = 8
Also, if 2 and 6 are selected together, the product will be divisible by 4. This can be done in 2 ways.
Thus, total number of ways = 8 + 2 = 10.
The number of ways of selecting two numbers out of the 5 one after the other is 5*4 = 20
Thus, the required probability = 10/20 = 1/2.
Thus, the correct option is D.
General Discussion
08 Aug 2022, 02:54
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Bunuel
Total number of options without replacement \(= 5*4 = 20\)
We can form 3 cases here to determine favorable outcomes:
Case 1: Both even
First number has 3 options \((2,4,6)\)and second number has 2 options \(= 3*2 = 6\)
Case 2: First odd number followed by 4
First has 2 options (\(3,5\)) and second has 1 option (\(4\)) = \(= 2*1 = 2\)
Case 3: First number 4 and second number odd
First has 1 option and second has 2 options (same as above) = \(1*2 = 2\)
Favorable outcomes \(= 6+2+2 = 10\)
Probability = \(\frac{10}{20} = \frac{1}{2}\)
\(Answer - D\)
