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Dua buah dadu dilambungkan bersama-sama 1 kali. Peluang munculnya mata dadu berjumlah 4 atau bernomor sama adalah ...

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A. Acfreelance

Master Teacher

Mahasiswa/Alumni Universitas Indraprasta PGRI

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peluang munculnya mata dadu berjumlah 4 atau bernomor sama adalah  begin mathsize 14px style 2 over 9 end style.

Pembahasan

Jumlah ruang sampel 2 dadu:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight n left parenthesis straight S right parenthesis end cell equals cell 6 squared end cell row blank equals 36 end table end style  

Peluang mata dadu berjumlah 4: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell space left curly bracket open parentheses 1 comma space 3 close parentheses comma space open parentheses 2 comma space 2 close parentheses comma space open parentheses 3 comma 1 close parentheses right curly bracket end cell row cell straight n left parenthesis straight A right parenthesis end cell equals 3 row cell straight P left parenthesis straight A right parenthesis end cell equals cell fraction numerator straight n left parenthesis straight A right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction end cell row blank equals cell 3 over 36 end cell row blank equals cell 1 over 12 end cell end table end style 

Peluang mata dadu bernomor sama:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight B equals cell left curly bracket open parentheses 1 comma space 1 close parentheses comma space open parentheses 2 comma space 2 close parentheses comma space open parentheses 3 comma 3 close parentheses comma space open parentheses 4 comma space 4 close parentheses comma space open parentheses 5 comma 5 close parentheses comma space open parentheses 6 comma 6 close parentheses right curly bracket end cell row cell straight n left parenthesis straight B right parenthesis end cell equals 6 row cell straight P left parenthesis straight B right parenthesis end cell equals cell fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction end cell row blank equals cell 6 over 36 end cell row blank equals cell 1 over 6 end cell end table end style 

Peluang mata dadu berjumlah 4 dan bernomor sama: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight A intersection straight B right parenthesis end cell equals cell left curly bracket open parentheses 2 comma space 2 close parentheses right curly bracket end cell row cell straight n left parenthesis straight A intersection straight B right parenthesis end cell equals 1 row cell straight P left parenthesis straight A intersection straight B right parenthesis end cell equals cell fraction numerator straight n left parenthesis straight A intersection straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction end cell row blank equals cell 1 over 36 end cell end table end style 

Peluang mata dadu berjumlah 4 atau bernomor sama: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight P left parenthesis straight A union straight B right parenthesis end cell equals cell straight P left parenthesis straight A right parenthesis plus straight P left parenthesis straight B right parenthesis minus straight P left parenthesis straight A intersection straight B right parenthesis end cell row blank equals cell 1 over 12 plus 1 over 6 minus 1 over 36 end cell row blank equals cell fraction numerator 3 plus 6 minus 1 over denominator 36 end fraction end cell row blank equals cell 8 over 36 end cell row blank equals cell 2 over 9 end cell end table end style  

Jadi, peluang munculnya mata dadu berjumlah 4 atau bernomor sama adalah  begin mathsize 14px style 2 over 9 end style.

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