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Dua puluh tujuh buah kartu dituliskan bilangan 1 sampai 27. Diambil satu buah kartu secara acak. Peluang terpilih kartu yang tertulis bilangan prima atau bilangan ganjil adalah ....

Dua puluh tujuh buah kartu dituliskan bilangan 1 sampai 27. Diambil satu buah kartu secara acak. Peluang terpilih kartu yang tertulis bilangan prima atau bilangan ganjil adalah ....

Jawaban:

Dengan menggunakan konsep peluang kejadian majemuk, maka peluang dapat dicari dengan cara sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight A equals cell Bilangan space prima space 1 space sampai space 27 end cell row blank equals cell open curly brackets 2 comma space 3 comma space 5 comma space 7 comma space 11 comma space 13 comma space 17 comma space 19 comma space 23 close curly brackets end cell row cell straight n left parenthesis straight A right parenthesis end cell equals 9 row blank blank blank row straight B equals cell Bilangan space ganjil space 1 space sampai space 27 end cell row blank equals cell open curly brackets 1 comma space 3 comma space 5 comma space 7 comma space 9 comma space 11 comma space 13 comma space 15 comma space 17 comma space 19 comma space 21 comma space 23 comma space 25 comma space 27 close curly brackets end cell row cell straight n left parenthesis straight B right parenthesis end cell equals 14 row blank blank blank row cell straight A intersection straight B end cell equals cell open curly brackets 3 comma space 5 comma space 7 comma space 11 comma space 13 comma space 17 comma space 19 comma space 23 close curly brackets end cell row cell straight n left parenthesis straight A intersection straight B right parenthesis end cell equals 8 row cell straight n left parenthesis straight S right parenthesis end cell equals 27 row blank blank blank 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 9 over 27 end cell 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 14 over 27 end cell 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 8 over 27 end cell row blank blank blank row cell straight P open parentheses straight A union straight B close parentheses 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 9 over 27 plus 14 over 27 minus 8 over 27 end cell row blank equals cell 15 over 27 end cell row blank equals cell 5 over 9 end cell end table end style

Jadi, Peluang terpilih kartu yang tertulis bilangan prima atau bilangan ganjil adalah begin mathsize 14px style 5 over 9 end style.

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