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SMK Teknologi dan Rekayasa

Soal 99 Permutasi-Kombinasi-Peluang


Dalam\ botol\ pertama\ terdapat\ 2\ tablet\ merah\ dan\ 3\ tablet\ putih.\\Dalam\ botol\ kedua\ terdapat\ 3\ tablet\ merah\ dan\ 4\ tablet\ putih.\\Dari\ masing-masing\ botol\ diambil\ satu\ tablet.\ Peluang\ kedua\ tablet\\yang\ terambil\ berwarna\ merah\ adalah\ ....
a.\ \ \frac{1}{35}\ \ \ \ \ \ \ \ \ \ b.\ \ \frac{3}{35}\ \ \ \ \ \ \ \ \ \ c.\ \ \frac{4}{35}\ \ \ \ \ \ \ \ \ \ d.\ \ \frac{5}{35}\ \ \ \ \ \ \ \ \ \ e.\ \ \frac{6}{35}
Jawaban: e

\mathbf{Pada\ botol\ pertama}:\\n(S)=_{5}C_{1}=5\\n(A)=_{2}C_{1}=2
P(A)=\frac{n(A)}{n(S)}=\frac{2}{5}
\mathbf{Pada\ botol\ kedua}:\\n(S)=_{7}C_{1}=7\\n(B)=_{3}C_{1}=3
P(B)=\frac{n(B)}{n(S)}=\frac{3}{7}
Peluang\ kedua\ tablet\ yang\ terambil\ berwarna\ merah\ adalah
\begin{array}{rcl}P(A\cap B)&=&P(A)\times P(B)\\\\&=&\frac{2}{5}\times \frac{3}{7}\\\\&=&\frac{6}{35}\end{array}

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