7.6.a 7.6.c 7.6.d 7.6.e 7.6.F* 7.6.h 7.6.I 7.12.b

Probability 7th Grade

Texas Essential Knowledge and Skills (TEKS): 7.6.a
represent sample spaces for simple and compound events using lists and tree diagrams;
Texas Essential Knowledge and Skills (TEKS): 7.6.c
make predictions and determine solutions using experimental data for simple and compound events;
Texas Essential Knowledge and Skills (TEKS): 7.6.d
make predictions and determine solutions using theoretical probability for simple and compound events;
Texas Essential Knowledge and Skills (TEKS): 7.6.e
find the probabilities of a simple event and its complement and describe the relationship between the two;
Texas Essential Knowledge and Skills (TEKS): 7.6.F*
use data from a random sample to make inferences about a population;
Texas Essential Knowledge and Skills (TEKS): 7.6.h
solve problems using qualitative and quantitative predictions and comparisons from simple experiments; and
Texas Essential Knowledge and Skills (TEKS): 7.6.I
determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.
Texas Essential Knowledge and Skills (TEKS): 7.12.b
use data from a random sample to make inferences about a population; and

Probability is a measure of the likelihood of an event occurring.

Probability of event occurring = \frac{number of ways event can occur}{total number of possible outcomes}

The sample space of an event occurring is the set of possible outcomes.

The complement of an event occurring is the event not occurring.
If the probability of an event occurring is P(A), then the complement is 1 − P(A), often denoted as P(A').

What is the probability Haley selects a blue token?

\begin{array}{rcl} Probability of event occurring & = & \frac{number of ways event can occur}{total number of possible outcomes} \\ = & \frac{7}{2 + 7 + 3} \\ = & \frac{7}{12} \end{array}

What is the probability Haley does not select a blue token?

The probability of an event not occurring is 1 minus the probability of the event occurring.

1 - \frac{7}{12} = \frac{5}{12}

Experimental probability is a measure of the
likelihood of an event occurring based on trials.

Experimental Probability = \frac{number of trials where event occurs}{total number of trials}

\begin{array}{rcl} Experimental Probability & = & \frac{number of trials where event occurs}{total number of trials} \\ = & \frac{6}{25} \end{array}

Probability can be used to make approximate predictions.

The spinner is divided into 6 equal sections, so the probability the spinner lands on each section is

\frac{1}{6}

Multiply

\frac{1}{6}

by 300 to predict the number of times the spinner will land on each section.

\frac{1}{6} \times 300 = 50

Since 50 is

\frac{1}{6}

of 300, the spinner would land on each section approximately 50 times.

Because this is a prediction, the spinner would probably not land on each section exactly 50 times.

Compound probability is a measure of the likelihood
that a combination of two or more events occurs.

Events are independent if the outcome of one event does not affect the outcome of another event, otherwise they are dependent events.

To find the probability of two independent events both occurring, multiply the probability of the first event by the probability of the second event.

The probability of the coin landing on heads is

\frac{1}{2}

The probability of the cube landing on an even number is

\frac{3}{6}

, which equals

\frac{1}{2}

Multiply the probabilities.

\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}

Probability

Texas Essential Knowledge and Skills (TEKS): 7.6.a

represent sample spaces for simple and compound events using lists and tree diagrams;

Texas Essential Knowledge and Skills (TEKS): 7.6.c

make predictions and determine solutions using experimental data for simple and compound events;

Texas Essential Knowledge and Skills (TEKS): 7.6.d

make predictions and determine solutions using theoretical probability for simple and compound events;

Texas Essential Knowledge and Skills (TEKS): 7.6.e

find the probabilities of a simple event and its complement and describe the relationship between the two;

Texas Essential Knowledge and Skills (TEKS): 7.6.F*

use data from a random sample to make inferences about a population;

Texas Essential Knowledge and Skills (TEKS): 7.6.h

solve problems using qualitative and quantitative predictions and comparisons from simple experiments; and

Texas Essential Knowledge and Skills (TEKS): 7.6.I

determine experimental and theoretical probabilities related to simple and compound events using data and sample spaces.

Texas Essential Knowledge and Skills (TEKS): 7.12.b

use data from a random sample to make inferences about a population; and

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