If a container of liquid contains 20 oz of solution, what is the number of ounces of pure acid if the given solution contains 20% acid concentrations?

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Ответ:

kat1357

17.06.2021

Mathematics

Follows are the solution to the given points:

Step-by-step explanation:

Given values:

$P(\frac{D}{A})=0.02 \\\\P(\frac{D}{B})=0.01\\\\P(A)=\frac{10,000}{10,000+2000} =\frac{10}{12} =\frac{5}{6} \\\\P(B)=\frac{1}{6}\\\\$

For point a:

$P(D) =p(D\cap A) +P(D \cap B)\\\\$

$=P(\frac{D}{A}) \times P(A) + P(\frac{D}{B}) \times P(B)\\\\=0.02 \times \frac{5}{6} + 0.01 \times \frac{1}{6}\\\\=\frac{0.1}{6} + \frac{0.01}{6}\\\\=\frac{0.1+0.01}{6} \\\\=\frac{0.11}{6} \\\\=\frac{11}{600} \\\\=0.0183$

For point b:

$P(\frac{A}{D})= \frac{P(\frac{D}{A}) \times P(A)}{P(D)}\\\\$

$= \frac{0.02 \times \frac{5}{6}}{\frac{11}{600}}\\\\= \frac{0.02 \times \frac{5}{6}}{0.0183333333}\\\\= \frac{0.02 \times 0.833333333}{0.0183333333}\\\\= \frac{0.0166666667}{0.018}\\\\=0.9090 \approx 0.0991$

For point c:

$P(\frac{A}{D^C})=\frac{P(\frac{D^c}{A}) \times P(A)}{P(D^c)}\\\\$

$= \frac{1-0.02 \times \frac{5}{6}}{1- \frac{11}{600}}\\\\= \frac{0.98 \times \frac{5}{6}}{0.98}\\\\=\frac{5}{6}\\\\=0.833$

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