When calculating probability, we are comparing the number of

favorable

o u t c o m e s

to the number of

possible

o u t c o m e s .

To calculate the probability that a randomly chosen letter tile is D we will use the Probability Formula.

P = \frac{Favorable Outcomes}{Possible Outcomes}

Let's take a look at the tiles.

There is a total of

9

letter tiles. This means that the number of

possible

outcomes

is

9 .

Out of these, there is

1

tile with D, which is the number of

favorable

outcomes .

Now we have enough information to calculate

P (D) .

P = \frac{Favorable Outcomes}{Possible Outcomes}

Substitute values

P (D) = \frac{1}{9}

The probability of choosing a D-tile is

\frac{1}{9} .

Next, we can rewrite the fraction as a decimal and as a percent.

To write a fraction as a decimal, we divide the numerator by the denominator.

The quotient is a repeating decimal, so we draw a horizontal bar on top of the repeated digits. We found that

\frac{1}{9}

expressed as a decimal is

0 . \overline{1} .

To write a fraction as a percent, we first find an equivalent fraction with a denominator of

100 .

\frac{1}{9} = \frac{p}{1 0 0}

Let's solve the equation for

p .

\frac{1}{9} = \frac{p}{1 0 0}

$LHS \cdot 100 = RHS \cdot 100$

\frac{1}{9} \cdot 100 = \frac{p}{1 0 0} \cdot 100

$\frac{a}{1 0 0} \cdot 100 = a$

\frac{1}{9} \cdot 100 = p

Write as a decimal

0.111111 \dots \cdot 100 = p

11.111111 \dots = p

Rearrange equation

p = 11.111111 \dots

The fraction written as a percent is

11 . \overline{1} % .

Exercise