Pertanyaan

Sebuah uang logam diundi 8 kali. Peluang diperoleh sisi angka (A) sebanyak 4 sampai 6 kali adalah ...

E. Dwi

Master Teacher

Mahasiswa/Alumni Universitas Sriwijaya

Jawaban terverifikasi

Jawaban

peluang diperoleh sisi angka (A) sebanyak 4 sampai 6 kali adalah .

peluang diperoleh sisi angka (A) sebanyak 4 sampai 6 kali adalah

Pembahasan

Jadi, peluang diperoleh sisi angka (A) sebanyak 4 sampai 6 kali adalah .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell C presubscript n subscript r end cell equals cell fraction numerator n factorial over denominator r factorial left parenthesis n minus r right parenthesis factorial end fraction end cell row cell C presubscript 8 subscript 4 end cell equals cell fraction numerator 8 factorial over denominator 4 factorial left parenthesis 8 minus 4 right parenthesis factorial end fraction end cell row cell C presubscript 8 subscript 4 end cell equals cell fraction numerator 8 cross times 7 cross times 6 cross times 5 cross times 4 factorial over denominator 4 factorial cross times 4 cross times 3 cross times 2 cross times 1 end fraction end cell row cell C presubscript 8 subscript 4 end cell equals cell 20 over 2 end cell row cell C presubscript 8 subscript 4 end cell equals 10 row cell C presubscript 8 subscript 5 end cell equals cell fraction numerator 8 factorial over denominator 5 factorial left parenthesis 8 minus 5 right parenthesis factorial end fraction end cell row cell C presubscript 8 subscript 5 end cell equals cell fraction numerator 8 cross times 7 cross times 6 cross times 5 factorial over denominator 5 factorial cross times 3 factorial end fraction end cell row cell C presubscript 8 subscript 5 end cell equals cell 112 over 2 end cell row cell C presubscript 8 subscript 5 end cell equals 56 row cell C presubscript 8 subscript 6 end cell equals cell fraction numerator 8 factorial over denominator 6 factorial left parenthesis 8 minus 6 right parenthesis factorial end fraction end cell row cell C presubscript 8 subscript 6 end cell equals cell fraction numerator 8 cross times 7 cross times 6 factorial over denominator 6 factorial cross times 2 factorial end fraction end cell row cell C presubscript 8 subscript 6 end cell equals cell 56 over 2 end cell row cell C presubscript 8 subscript 6 end cell equals 28 row cell n left parenthesis K right parenthesis end cell equals cell 10 plus 56 plus 28 equals 94 end cell end table end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell P left parenthesis K right parenthesis end cell equals cell fraction numerator n left parenthesis K right parenthesis over denominator n left parenthesis S right parenthesis end fraction end cell row blank equals cell 94 over 256 equals 47 over 128 end cell end table end style$

Jadi, peluang diperoleh sisi angka (A) sebanyak 4 sampai 6 kali adalah .

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