7th Grade · 7.SP.C.5

Probability in 7th grade

Probability is the math of chance, and 7th grade is the first year children study it as a topic of its own. A probability is a number from 0 to 1 that says how likely something is to happen. Your child learns to read that number, match it with words like unlikely and likely and compare the chances of two events.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around $\frac{1}{2}$ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

What it means, in plain words

An event is something that might happen, such as rolling a 5 on a number cube or rain tomorrow. Its probability is a number between 0 and 1. A probability of 0 means the event cannot happen. A probability of 1 means it is certain.

Your child places events on a probability scale, a line from 0 to 1. Events near 0 are unlikely. Events near $\frac{1}{2}$ are as likely to happen as not, like a fair coin landing heads. Events near 1 are likely. The bigger the number, the greater the likelihood, which is the chance that the event happens.

A probability can be a fraction, a decimal or a percent: $\frac{1}{4}$ , 0.25 and 25% are the same probability. To compare two probabilities written in different forms, your child first writes them in the same form, usually as decimals.

Your child should be able to:

Explain what a probability of 0, $\frac{1}{2}$ or 1 means
Match a probability with a word such as unlikely, as likely as not or likely
Place events on a probability scale from 0 to 1
Compare probabilities written as fractions, decimals and percents

Example

Which event is more likely: one with a probability of 0.65, or one with a probability of $\frac{3}{5}$ ?

Write the fraction as a decimal: $\frac{3}{5} = 3 \div 5 = 0.6$ .
Compare the decimals: $0.65 > 0.6$ .
The event with a probability of 0.65 is more likely.

Example

A weather forecast gives an 80% chance of rain. Where is that on the probability scale, and what does it mean?

80% is $\frac{80}{100}$ , or 0.8.
0.8 is close to 1, so rain is likely.
0.8 is less than 1, so rain is not certain. Rain is likely, but a dry day can still happen.

Where children usually get stuck

Your child gives a probability of 3, or 120%, for something that seems very likely.
Bigger numbers mean more likely, so the child keeps going past 1. The top of the scale, certain, is exactly 1.
What helps. Draw the scale from 0 to 1 and ask what could be more likely than certain. Nothing can, so no probability is greater than 1.
Your child says 0.25 is more likely than $\frac{1}{3}$ , because 25 is bigger than 3.
The child compares the digits on the page instead of the values. $\frac{1}{3}$ is about 0.33, which is bigger than 0.25.
What helps. Have your child write the fraction as a decimal first: $1 \div 3$ is about 0.33. Then compare 0.25 with 0.33.
Your child says an event with a probability of 0.1 will not happen.
Unlikely and impossible sound alike. Only a probability of 0 means an event cannot happen.
What helps. Ask how many times out of 10 the event happens. One time in 10 is rare, but it is not never.

Try four practice questions

Real 7th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Match each likelihood word to the probability that fits it best.
Connect each item on the left to its match on the right.
Likelihood word
Probability
unlikely
about 1/2
likely
$\displaystyle 0.7$
$\displaystyle 0.5$
$\displaystyle 0.1$
Use Tab to navigate between items. Click or tap a card to select it, then click or tap a card on the opposite side to create a match. You can also drag a card or its connector dot to a card on the opposite side.
Show the answer and how to solve it
The matches are unlikely → 0.1, about $\frac{1}{2}$ → 0.5, and likely → 0.7.
1. 1Find the probability equal to $\frac{1}{2}$ . Since $0.5 = \frac{1}{2}$ , match 0.5 to 'about $\frac{1}{2}$ '.
2. 2Compare the remaining values to 0.5.
3. 3In this set, $0.1$ is well below half, so it fits 'unlikely'. $0.7$ is well above half, so it fits 'likely'. $0.5$ equals half, so it fits 'about $\frac{1}{2}$ '.
Common mistake. A common mistake is swapping 0.1 and 0.7. Always compare each value to 0.5 first: 0.1 is well below 0.5, so it is unlikely; 0.7 is well above 0.5, so it is likely.
The idea underneath. At $\frac{1}{2}$ , an event is as likely to happen as not. Probabilities close to half fit 'about $\frac{1}{2}$ '. Probabilities well below or well above half fit 'unlikely' or 'likely'.
2On level
The probabilities below are not in order. Which choice lists the same probabilities from smallest to largest?
$\displaystyle \left\{\frac{1}{2},\ 0.1,\ 0.7,\ \frac{1}{4}\right\}$
A
$\displaystyle 0.1,\ \frac{1}{4},\ \frac{1}{2},\ 0.7$
B
$\displaystyle 0.7,\ \frac{1}{2},\ \frac{1}{4},\ 0.1$
C
$\displaystyle \frac{1}{4},\ 0.1,\ \frac{1}{2},\ 0.7$
D
$\displaystyle 0.1,\ \frac{1}{4},\ 0.7,\ \frac{1}{2}$
Show the answer and how to solve it
The correct order is $0.1, \frac{1}{4}, \frac{1}{2}, 0.7$ because $\frac{1}{4} = 0.25$ and $\frac{1}{2} = 0.5$ .
1. 1Start by comparing the four probabilities in the set.
2. 2Rewrite the fractions as decimals so all values are on the same 0-to-1 scale.
3. 3Now order all four probabilities from least to greatest.
4. 4Select the option that shows that exact order.
Common mistake. A common mistake is placing $\frac{1}{4}$ before $0.1$ because the fraction looks small. But $\frac{1}{4} = 0.25$ , which is greater than $0.1$ , so $0.1$ must come first.
The idea underneath. Fractions and decimals can be ordered together once you compare them on the same 0-to-1 probability scale.
3On level
Which word best matches the probability below?
$\displaystyle \frac{2}{4}$
A
unlikely
B
about $\frac{1}{2}$
C
likely
Show the answer and how to solve it
The answer is about $\frac{1}{2}$ because $\frac{2}{4}$ is the same as $\frac{1}{2}$ .
1. 1Look at the probability shown.
2. 2 $\frac{2}{4}$ means 2 out of 4, which is exactly half.
3. 3A value that is exactly half is best described as about $\frac{1}{2}$ .
Common mistake. A common mistake is treating any proper fraction as unlikely. Compare the fraction to $\frac{1}{2}$ first: $\frac{2}{4}$ equals $\frac{1}{2}$ exactly, so it is not low.
The idea underneath. Likelihood words are benchmark descriptions on the 0-to-1 scale: values near 0 are unlikely, values near $\frac{1}{2}$ are about $\frac{1}{2}$ , and values near 1 are likely.
4Stretch
Type the greatest whole-number numerator so the fraction below could represent a probability but not 1.
$\displaystyle 6$
Show the answer and how to solve it
Answer. 5
The only correct answer is $5$ because $\frac{5}{6}$ is the greatest fraction with denominator $6$ that is a valid probability but not $1$ .
1. 1The numerator is the box you type into; the denominator is fixed at $6$ . A probability must be between $0$ and $1$ , inclusive.
2. 2With denominator $6$ , the whole-number numerator must be at least $0$ and at most $6$ for the fraction to stay in $[0, 1]$ .
3. 3The prompt says the fraction cannot equal $1$ . Since $\frac{6}{6} = 1$ , the numerator $6$ is not allowed.
4. 4After removing $6$ , the remaining candidates are $0, 1, 2, 3, 4, 5$ . The greatest of these is $5$ . Since $\frac{5}{6} < 1$ , it is a valid probability.
5. 5Typing $5$ into the numerator box gives $\frac{5}{6}$ , which satisfies $0 \le \frac{5}{6} \le 1$ and is not equal to $1$ , so $5$ is the answer.
Common mistake. A common mistake is typing $6$ as the greatest numerator. But $\frac{6}{6} = 1$ , and the prompt excludes $1$ , so $6$ is not allowed.
The idea underneath. For a fraction with a positive denominator to represent a probability, the whole-number numerator must stay between 0 and the denominator, unless the prompt removes one endpoint.