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1-55.

Probability is used to make predictions. See the Math Notes in this lesson for more details. Whenever the outcomes are equally likely, the probability in general is:

$\text{P(success)}=\large{\frac{\text{number of success}}{\text{total number of possible outcomes}}}$

For example, if you were to reach into a bag with $16$ total shapes, four of which have right angles, and randomly pull out a shape, you could use probability to predict the chances of the shape having a right angle.

$\begin{equation} \text{P(right angle)}=\large{\frac{\text{number of success}}{\text{total number of possible outcomes}}}\\ \qquad \qquad \qquad \, =\large{\frac{\text{4 shapes with right angles}}{\text{16 total shapes}}}\\ \qquad \qquad \qquad \, =\large\frac{4}{16}=\frac{1}{4}=0.25=25\% \end{equation}$

The example above shows all forms of writing probability: $\large\frac { 4 } { 16 }$ (read “$4\text{ out of }16$”) is the probability as a ratio, $0.25$ is its decimal form, and $25$% is its equivalent percent. What else can probability be used to predict? Analyze each of the situations below:

Use the P(success) formula above to solve parts (a-d).

1. The historic carousel at the park has $4$ giraffes, $4$ lions, $2$ elephants, $18$ horses, $1$ monkey, $6$ unicorns, $3$ ostriches, $3$ zebras, $6$ gazelles, and even $1$ dinosaur. Eric’s niece wants for Eric to randomly pick an animal to ride. What is the probability (expressed as a percent) that Eric picks a horse, a unicorn, or a zebra?

$\frac{27}{48}\approx56.3\%$

2. Eduardo has in his pocket $1 in pennies,$1 in nickels, and \$1 in dimes. If he randomly pulls out just one coin, what is the probability that he will pull out a dime?

$\frac{10}{130}=\frac{1}{13}\approx8\%$

3. $P(\text{rolling an }8)$ with one regular die if you roll the die just once.

$0$

4. P(dart hitting a shaded region) if the dart is randomly thrown and hits the target at right.

$\frac{5}{9}\approx56\%$

 shaded tile $\space$ tile $\space$ shaded tile $\space$ tile $\space$ shaded tile $\space$ tile $\space$ shaded tile $\space$ tile $\space$ shaded tile $\space$

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