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Dalam survei di sebuah sekolah menengah atas, diketahui 60% siswa pernah menyontek dalam ujian akhir semester. Jika dipilih 15 siswa secara acak, maka peluang tidak lebih dari 5 siswa pernah menyontekadalah ....

Dalam survei di sebuah sekolah menengah atas, diketahui 60% siswa pernah menyontek dalam ujian akhir semester. Jika dipilih 15 siswa secara acak, maka peluang tidak lebih dari 5 siswa pernah menyontek adalah ....space 

  1. 0,034 space 

  2. 0,095 space 

  3. 0,213 space 

  4. 0,390 space 

  5. 0,597 space 

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N. Puspita

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Dari kasus di atas, diperoleh Ingat bahwa Sehingga dapat diperoleh 1. 2. 3. 4. 5. 6. Akibatnya, didapat Artinya, jika dipilih 15 siswa secara acak, maka peluang tidak lebih dari 5 siswa pernah menyontekadalah Oleh karena itu, tidak ada pilihan jawaban yang tepat.

Dari kasus di atas, diperoleh

  • n equals banyak space percobaan equals 15
  • x equals open curly brackets 0 comma space 1 comma space 2 comma space 3 comma space 4 comma space 5 close curly brackets
  • begin mathsize 12px style p equals peluang space siswa space pernah space menyontek equals 60 percent sign equals 0 comma 6 end style
  • begin mathsize 11px style 1 minus p equals peluang space siswa space tidak space pernah space menyontek equals 1 minus 0 comma 6 equals 0 comma 4 end style 

Ingat bahwa

P open parentheses X equals x close parentheses equals C presubscript n subscript x cross times p to the power of x cross times open parentheses 1 minus p close parentheses to the power of n minus x end exponent

Sehingga dapat diperoleh

1. table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell equals cell 0 right parenthesis equals C presubscript 15 subscript 0 cross times open parentheses 0 comma 6 close parentheses to the power of 0 cross times open parentheses 0 comma 4 close parentheses to the power of 15 minus 0 end exponent end cell row blank equals cell fraction numerator 15 factorial over denominator left parenthesis 15 minus 0 right parenthesis factorial cross times 0 factorial end fraction cross times 1 cross times open parentheses 0 comma 4 close parentheses to the power of 15 end cell row blank equals cell 1 cross times open parentheses 0 comma 4 close parentheses to the power of 15 end cell row blank equals cell 0 comma 0000010737 end cell end table 

 

2. table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell equals cell 1 right parenthesis equals C presubscript 15 subscript 1 cross times open parentheses 0 comma 6 close parentheses to the power of 1 cross times open parentheses 0 comma 4 close parentheses to the power of 15 minus 1 end exponent end cell row blank equals cell fraction numerator 15 factorial over denominator left parenthesis 15 minus 1 right parenthesis factorial cross times 1 factorial end fraction cross times 0 comma 6 cross times open parentheses 0 comma 4 close parentheses to the power of 14 end cell row blank equals cell fraction numerator 15 cross times 14 factorial over denominator 14 factorial cross times 1 end fraction cross times 0 comma 6 cross times open parentheses 0 comma 4 close parentheses to the power of 14 end cell row blank equals cell 0 comma 00002415919104 end cell end table 

 

3. table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell equals cell 2 right parenthesis equals C presubscript 15 subscript 2 cross times open parentheses 0 comma 6 close parentheses squared cross times open parentheses 0 comma 4 close parentheses to the power of 15 minus 2 end exponent end cell row blank equals cell fraction numerator 15 factorial over denominator left parenthesis 15 minus 2 right parenthesis factorial cross times 2 factorial end fraction cross times open parentheses 0 comma 6 close parentheses squared cross times open parentheses 0 comma 4 close parentheses to the power of 13 end cell row blank equals cell fraction numerator 15 cross times 14 cross times 13 factorial over denominator 13 factorial cross times 2 cross times 1 end fraction cross times open parentheses 0 comma 6 close parentheses squared cross times open parentheses 0 comma 4 close parentheses to the power of 13 end cell row blank equals cell 0 comma 0002536715059 end cell end table 

 

4. table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell equals cell 3 right parenthesis equals C presubscript 15 subscript 3 cross times open parentheses 0 comma 6 close parentheses cubed cross times open parentheses 0 comma 4 close parentheses to the power of 15 minus 3 end exponent end cell row blank equals cell fraction numerator 15 factorial over denominator left parenthesis 15 minus 3 right parenthesis factorial cross times 3 factorial end fraction cross times open parentheses 0 comma 6 close parentheses cubed cross times open parentheses 0 comma 4 close parentheses to the power of 12 end cell row blank equals cell fraction numerator 15 cross times 14 cross times 13 cross times 12 factorial over denominator 12 factorial cross times 3 cross times 2 cross times 1 end fraction cross times open parentheses 0 comma 6 close parentheses cubed cross times open parentheses 0 comma 4 close parentheses to the power of 12 end cell row blank equals cell 0 comma 00164886487884 end cell end table   

 

5. table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell equals cell 4 right parenthesis equals C presubscript 15 subscript 4 cross times open parentheses 0 comma 6 close parentheses to the power of 4 cross times open parentheses 0 comma 4 close parentheses to the power of 15 minus 4 end exponent end cell row blank equals cell fraction numerator 15 factorial over denominator left parenthesis 15 minus 4 right parenthesis factorial cross times 4 factorial end fraction cross times open parentheses 0 comma 6 close parentheses to the power of 4 cross times open parentheses 0 comma 4 close parentheses to the power of 11 end cell row blank equals cell fraction numerator 15 cross times 14 cross times 13 cross times 12 cross times 11 factorial over denominator 11 factorial cross times 4 cross times 3 cross times 2 cross times 1 end fraction cross times open parentheses 0 comma 6 close parentheses to the power of 4 cross times open parentheses 0 comma 4 close parentheses to the power of 11 end cell row blank equals cell 0 comma 0074198915481 end cell end table  

 

6.  table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis X end cell equals cell 5 right parenthesis equals C presubscript 15 subscript 5 cross times open parentheses 0 comma 6 close parentheses to the power of 5 cross times open parentheses 0 comma 4 close parentheses to the power of 15 minus 5 end exponent end cell row blank equals cell fraction numerator 15 factorial over denominator left parenthesis 15 minus 5 right parenthesis factorial cross times 5 factorial end fraction cross times open parentheses 0 comma 6 close parentheses to the power of 5 cross times open parentheses 0 comma 4 close parentheses to the power of 10 end cell row blank equals cell fraction numerator 15 cross times 14 cross times 13 cross times 12 cross times 11 cross times 10 factorial over denominator 10 factorial cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 end fraction cross times open parentheses 0 comma 6 close parentheses to the power of 5 cross times open parentheses 0 comma 4 close parentheses to the power of 10 end cell row blank equals cell 0 comma 0244856421089 end cell end table  

Akibatnya, didapat

begin mathsize 12px style P left parenthesis X less or equal than 5 right parenthesis equals P open parentheses X equals 0 close parentheses plus P open parentheses X equals 1 close parentheses plus P open parentheses X equals 2 close parentheses plus P open parentheses X equals 3 close parentheses plus P open parentheses X equals 4 close parentheses plus P open parentheses X equals 5 close parentheses equals 0 comma 0338333028423 end style    

Artinya, jika dipilih 15 siswa secara acak, maka peluang tidak lebih dari 5 siswa pernah menyontek adalah begin mathsize 12px style 0 comma 0338333028423 end style

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