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Seorang siswa sedang menghadapi kuis matematika. Kuis terdiri atas 7 soal pilihan ganda dengan 4 pilihan. Karena kuis mendadak maka siswa tersebut meniawab seluruh soal dengan cara menebak. Berapa peluang siswa tersebut menjawab: b. paling banyak 4 soal.

Pertanyaan

Seorang siswa sedang menghadapi kuis matematika. Kuis terdiri atas 7 soal pilihan ganda dengan 4 pilihan. Karena kuis mendadak maka siswa tersebut meniawab seluruh soal dengan cara menebak. Berapa peluang siswa tersebut menjawab:

b. paling banyak 4 soal. 

A. Salim

Master Teacher

Mahasiswa/Alumni Universitas Pelita Harapan

Jawaban terverifikasi

Jawaban

peluang siswa tersebut menjawab paling banyak 4 soal yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6993 over 8192 end cell end table end style.

Pembahasan

Dengan menggunakan distribusi binomial, maka didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row p equals cell peluang space benar end cell row blank equals cell 1 fourth end cell row q equals cell peluang space salah end cell row blank equals cell 1 minus p end cell row blank equals cell 1 minus 1 fourth end cell row blank equals cell 3 over 4 end cell row blank blank blank row cell P open parentheses 1 close parentheses end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 7 subscript 1 cross times open parentheses 1 fourth close parentheses to the power of 1 cross times open parentheses 3 over 4 close parentheses to the power of 7 minus 1 end exponent end cell row blank equals cell fraction numerator 7 factorial over denominator left parenthesis 7 minus 1 right parenthesis factorial 1 factorial end fraction cross times open parentheses 1 fourth close parentheses to the power of 1 cross times open parentheses 3 over 4 close parentheses to the power of 6 end cell row blank equals cell fraction numerator 7 cross times 6 factorial over denominator 6 factorial cross times 1 end fraction cross times 1 fourth cross times 729 over 4096 end cell row blank equals cell 7 cross times 729 over 16384 end cell row blank equals cell 5103 over 16384 end cell row blank blank blank row cell P open parentheses 2 close parentheses end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 7 subscript 2 cross times open parentheses 1 fourth close parentheses squared cross times open parentheses 3 over 4 close parentheses to the power of 7 minus 2 end exponent end cell row blank equals cell fraction numerator 7 factorial over denominator left parenthesis 7 minus 2 right parenthesis factorial 2 factorial end fraction cross times open parentheses 1 fourth close parentheses squared cross times open parentheses 3 over 4 close parentheses to the power of 5 end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 factorial over denominator 5 factorial cross times 2 cross times 1 end fraction cross times 1 over 16 cross times 243 over 1024 end cell row blank equals cell 21 cross times 243 over 16384 end cell row blank equals cell 5103 over 16384 end cell row blank blank blank row cell P open parentheses 3 close parentheses end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 7 subscript 3 cross times open parentheses 1 fourth close parentheses cubed cross times open parentheses 3 over 4 close parentheses to the power of 7 minus 3 end exponent end cell row blank equals cell fraction numerator 7 factorial over denominator left parenthesis 7 minus 3 right parenthesis factorial 3 factorial end fraction cross times open parentheses 1 fourth close parentheses cubed cross times open parentheses 3 over 4 close parentheses to the power of 4 end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 cross times 4 factorial over denominator 4 factorial cross times 3 cross times 2 cross times 1 end fraction cross times 1 over 64 cross times 81 over 256 end cell row blank equals cell 35 cross times 81 over 16384 end cell row blank equals cell 2835 over 16384 end cell row blank blank blank row cell P open parentheses 4 close parentheses end cell equals cell C presubscript n subscript r cross times p to the power of r cross times q to the power of n minus r end exponent end cell row blank equals cell C presubscript 7 subscript 4 cross times open parentheses 1 fourth close parentheses to the power of 4 cross times open parentheses 3 over 4 close parentheses to the power of 7 minus 4 end exponent end cell row blank equals cell fraction numerator 7 factorial over denominator left parenthesis 7 minus 4 right parenthesis factorial 4 factorial end fraction cross times open parentheses 1 fourth close parentheses to the power of 4 cross times open parentheses 3 over 4 close parentheses cubed end cell row blank equals cell fraction numerator 7 cross times 6 cross times 5 cross times 4 factorial over denominator 3 cross times 2 cross times 1 cross times 4 factorial end fraction cross times 1 over 256 cross times 27 over 64 end cell row blank equals cell 35 cross times 27 over 16384 end cell row blank equals cell 945 over 16384 end cell row blank blank blank row peluang equals cell 5103 over 16384 plus 5103 over 16384 plus 2835 over 16384 plus 945 over 16384 end cell row blank equals cell 13986 over 16384 end cell row blank equals cell 6993 over 8192 end cell end table end style

Jadi, peluang siswa tersebut menjawab paling banyak 4 soal yaitu begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 6993 over 8192 end cell end table end style.

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Tujuh uang logam seimbang dilantunkan. Tentukan probabilitas: a. munculnya sisi gambar tepat lima kali. b.munculnya sisi gambar sedikitnya 4 kali. c. munculnya sisi gambar paling banyak 2 kali.

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