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A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is a  Short Answer Type Questions as classified in NCERT Exemplar

    Sol:

    Here,  we  have  X=0, 1, 2, 3         [?  die  is  thrown  3  times]and  p=16,  q=1−16=56∴  P(X=0)=P(not 2).P(not 2).P(not 2)=56.56.56=125216      P(X=1)=P(2).P(2).P(not 2)+P(2).P(not 2).P(2)+P(not 2).P(2).P(2)                            =16.16.56+16.56.16+56.16.16=5216+5216+5216=15216       P(X=3)=P(2).P(2).P(2)=16.16.16=1216Now,    E(X)=∑i=1npixi                              =0×125216+1×75216+2×15216+3×1216                              =0+75216+30216+3216=75+30+3216=108216=12Hence,  the  required    is  12.

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