Linear Inequalities

Question
CBSEENMA11015513

Three numbers are chosen at random without replacement from {1, 2, 3, ...... 8}. The probability that their minimum is 3, given that their maximum is 6, is

  • 3/8

  • 1/5

  • 1/4

  • 2/5

Solution

B.

1/5

Let A be the event that maximum is 6.
B be event that minimum is 3
straight P space left parenthesis straight A right parenthesis space equals space fraction numerator straight C presuperscript 5 subscript 2 over denominator straight C presuperscript 8 subscript 3 end fraction space left parenthesis the space numbers space less than space 6 space are space 5 right parenthesis
straight P left parenthesis straight B right parenthesis space equals space fraction numerator straight C presuperscript 5 subscript 2 over denominator straight C presuperscript 8 subscript 3 end fraction space left parenthesis the space numbers space greater than space 3 space are space 5 right parenthesis
straight P space left parenthesis straight A space intersection straight B right parenthesis space equals space fraction numerator straight C presuperscript 2 subscript 1 over denominator straight C presuperscript 8 subscript 3 end fraction
Required probability is straight P space open parentheses straight B over straight A close parentheses space equals space fraction numerator straight p space left parenthesis straight A space intersection straight B right parenthesis over denominator straight P space left parenthesis straight A right parenthesis end fraction space equals space fraction numerator straight C presuperscript 2 subscript 1 over denominator straight C presuperscript 5 subscript 2 end fraction space equals space 2 over 10 space equals space 1 fifth

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