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Dua dadu berwarna merah dan biru dilempar bersama. Misalkan  adalah kejadian muncul jumlah kedua mata dadu 9,  adalah kejadian muncul jumlah kedua mata dadu 3,  adalah kejadian muncul selisih kedua mata dadu 1. Tentukan nilai .

Pertanyaan

Dua dadu berwarna merah dan biru dilempar bersama. Misalkan size 14px A adalah kejadian muncul jumlah kedua mata dadu 9, size 14px B adalah kejadian muncul jumlah kedua mata dadu 3, begin mathsize 14px style C end style adalah kejadian muncul selisih kedua mata dadu 1. Tentukan nilai begin mathsize 14px style P open parentheses C vertical line A close parentheses space dan space P open parentheses C vertical line B close parentheses end style.

Pembahasan Soal:

Nilai begin mathsize 14px style P open parentheses C vertical line A close parentheses space dan space P open parentheses C vertical line B close parentheses end style dapat dicari dengan rumus peluang bersyarat berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell P open parentheses X vertical line Y close parentheses end cell equals cell fraction numerator P open parentheses X intersection Y close parentheses over denominator P open parentheses Y close parentheses end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator n left parenthesis X intersection Y right parenthesis over denominator n open parentheses S close parentheses end fraction end style over denominator begin display style fraction numerator n left parenthesis Y right parenthesis over denominator n left parenthesis S right parenthesis end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style n left parenthesis X intersection Y right parenthesis end style over denominator begin display style n left parenthesis Y right parenthesis end style end fraction end cell row blank blank blank row A equals cell open curly brackets open parentheses 3 comma space 6 close parentheses comma space open parentheses 4 comma space 5 close parentheses comma space open parentheses 5 comma space 4 close parentheses comma space open parentheses 6 comma space 3 close parentheses close curly brackets end cell row B equals cell open curly brackets open parentheses 1 comma space 2 close parentheses comma space open parentheses 2 comma space 1 close parentheses close curly brackets end cell row C equals cell open curly brackets open parentheses 1 comma space 2 close parentheses comma space open parentheses 2 comma space 1 close parentheses comma space open parentheses 2 comma space 3 close parentheses comma space open parentheses 3 comma space 2 close parentheses comma space open parentheses 3 comma space 4 close parentheses comma space open parentheses 4 comma space 3 close parentheses comma space open parentheses 4 comma space 5 close parentheses comma space open parentheses 5 comma space 4 close parentheses comma space open parentheses 5 comma space 6 close parentheses comma space open parentheses 6 comma space 5 close parentheses close curly brackets end cell row cell n open parentheses A close parentheses end cell equals 4 row cell n left parenthesis B right parenthesis end cell equals 2 row cell n left parenthesis C right parenthesis end cell equals 10 row cell n left parenthesis A intersection C right parenthesis end cell equals 2 row cell n left parenthesis B intersection C right parenthesis end cell equals 2 row blank blank blank row cell P open parentheses C vertical line A close parentheses end cell equals cell fraction numerator P open parentheses A intersection C close parentheses over denominator P open parentheses A close parentheses end fraction end cell row blank equals cell fraction numerator begin display style n left parenthesis A intersection C right parenthesis end style over denominator begin display style n left parenthesis A right parenthesis end style end fraction end cell row blank equals cell fraction numerator begin display style 2 end style over denominator begin display style 4 end style end fraction end cell row blank equals cell 1 half end cell row blank blank blank row cell P open parentheses C vertical line B close parentheses end cell equals cell fraction numerator P open parentheses B intersection C close parentheses over denominator P open parentheses B close parentheses end fraction end cell row blank equals cell fraction numerator begin display style n left parenthesis B intersection C right parenthesis end style over denominator begin display style n left parenthesis B right parenthesis end style end fraction end cell row blank equals cell fraction numerator begin display style 2 end style over denominator begin display style 2 end style end fraction end cell row blank equals 1 end table

Jadi, nilai dari begin mathsize 14px style P left parenthesis C vertical line A right parenthesis equals 1 half end style dan nilai dari begin mathsize 14px style P left parenthesis C vertical line B right parenthesis equals 1 end style.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 19 Juni 2021

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