If three numbers are chosen randomly from the set { 1 , 3 , 3 2 , … . , 3 n } without replacement, then the probability that they form an increasing geometric progression is

Number of triplets ( 3 r , 3 r + 1 , 3 r + 2 ) ( 0 ≤ r ≤ n ) is n − 1 Number of triplets ( 3 r , 3 r + 2 , 3 r + 4 ) ( 0 ≤ r ≤ n ) is n − 3 ____

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Mathematics - Probability Question with Solution | TestHub

MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Hard2 minQB

MathematicsHardmultiple choice

If three numbers are chosen randomly from the set ${1, 3, 3^{2}, \dots ., 3^{n}}$ without replacement, then the probability that they form an increasing geometric progression is

Options:(select one or more)

Answer:

A, C

Solution:

Number of triplets $(3^{r}, 3^{r + 1}, 3^{r + 2}) (0 \leq r \leq n)$ is $n - 1$ Number of triplets $(3^{r}, 3^{r + 2}, 3^{r + 4}) (0 \leq r \leq n)$ is $n - 3$ $____$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: QB

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