ProbabilityHardBloom L3
Question
Three numbers are selected one by one at random without replacement from the set of numbers $\{ 1,2,3,\ldots\ldots,n\}$. Then the probability that the third number lies between the first two, if the first number is known to be smaller than the second is equal to :
Options
A.$\frac{1}{6}$
B.$\frac{1}{2}$
C.$\frac{1}{3}$
D.$\frac{1}{4}$
Solution
Sol. [Key Concept: Three numbers one-by-one without replacement: probability of the order.]
$$\mathbf{P} = \frac{\ ^{n}C_{3} \times 1}{\ ^{n}C_{3} \times 3} = \frac{1}{3}$$
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