Solve P(c)=2/8*1/2+2/8*(1-1/2)+(1-frac{2}{8})*frac{1}{2}

$$P ( c ) = \frac { 2 } { 8 } \times \frac { 1 } { 2 } + \frac { 2 } { 8 } \times ( 1 - \frac { 1 } { 2 } ) + ( 1 - \frac { 2 } { 8 } ) \times \frac { 1 } { 2 }$$

Evaluate

$$\frac{5}{8}=0.625$$

Solution Steps

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}\times \frac{1}{2}+\frac{2}{8}\left(1-\frac{1}{2}\right)+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Multiply \frac{1}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{4\times 2}+\frac{2}{8}\left(1-\frac{1}{2}\right)+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 2}.

$$\frac{1}{8}+\frac{2}{8}\left(1-\frac{1}{2}\right)+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{8}+\frac{1}{4}\left(1-\frac{1}{2}\right)+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Convert 1 to fraction \frac{2}{2}.

$$\frac{1}{8}+\frac{1}{4}\left(\frac{2}{2}-\frac{1}{2}\right)+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{8}+\frac{1}{4}\times \frac{2-1}{2}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Subtract 1 from 2 to get 1.

$$\frac{1}{8}+\frac{1}{4}\times \frac{1}{2}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Multiply \frac{1}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{8}+\frac{1\times 1}{4\times 2}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Do the multiplications in the fraction \frac{1\times 1}{4\times 2}.

$$\frac{1}{8}+\frac{1}{8}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Since \frac{1}{8} and \frac{1}{8} have the same denominator, add them by adding their numerators.

$$\frac{1+1}{8}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Add 1 and 1 to get 2.

$$\frac{2}{8}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\left(1-\frac{2}{8}\right)\times \frac{1}{2}$$

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}+\left(1-\frac{1}{4}\right)\times \frac{1}{2}$$

Convert 1 to fraction \frac{4}{4}.

$$\frac{1}{4}+\left(\frac{4}{4}-\frac{1}{4}\right)\times \frac{1}{2}$$

Since \frac{4}{4} and \frac{1}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}+\frac{4-1}{4}\times \frac{1}{2}$$

Subtract 1 from 4 to get 3.

$$\frac{1}{4}+\frac{3}{4}\times \frac{1}{2}$$

Multiply \frac{3}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}+\frac{3\times 1}{4\times 2}$$

Do the multiplications in the fraction \frac{3\times 1}{4\times 2}.

$$\frac{1}{4}+\frac{3}{8}$$

Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{3}{8} to fractions with denominator 8.

$$\frac{2}{8}+\frac{3}{8}$$

Since \frac{2}{8} and \frac{3}{8} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{8}$$

Add 2 and 3 to get 5.

$$\frac{5}{8}$$

Factor

$$\frac{5}{2 ^ {3}} = 0.625$$