7th grade · Math · Unit 12 of 22
Probability
Chances of two events
What your child practices
Listing outcomes of two independent events (like a coin and a die), finding theoretical probabilities by multiplying, and comparing them with experimental results.
Texas Essential Knowledge and Skills (TEKS) teks student expectation: 7.6(A); 7.6(D); 7.6(I) · sample spaces and theoretical probability of simple and compound events
How we explain it
Children can open this short lesson before they practice.
- Probability = favorable outcomes ÷ all possible outcomes.
- It is always between 0 (impossible) and 1 (certain).
- For two events, list every outcome so none are missed.
Example: You roll a die. What is the probability of an even number? Even numbers: 2, 4, 6. That is 3 outcomes. There are 6 outcomes in all. 3/6 = 1/2. Answer: 1/2
Probability in Texas
In the Texas Essential Knowledge and Skills (TEKS), this is unit 12 of 22 in 7th grade Math, after Nets & Surface Area and before Dependent Events.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Source: Texas Education Agency (TEA)
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Two spinners are each half red and half blue. Priya spun both 25 times, and both landed on red 7 times. What is the experimental probability of "both red" as a percent?
answer box%
28 %
Hint: Experimental probability = 7/25 = 0.28 = 28%. Compare it with the theoretical probability: 1/2 × 1/2 = 1/4 = 25%.
Question 2
The table shows every outcome of flipping a coin (H or T) and rolling a die. How many outcomes show a 5 or a 6 (with either coin side)?
Coin 1 2 3 4 5 6 H H1 H2 H3 H4 H5 H6 T T1 T2 T3 T4 T5 T6 answer box
4
Hint: Find the matching cells: H5, H6, T5, T6. That's 4 of the 12 outcomes.
Question 3
You spin this spinner (4 equal sections) and flip a coin. What is P(blue and tails)?
- 2/6
- 1/8
- 3/4
- 1/4
1/8
Hint: P(blue) = 1/4 and P(tails) = 1/2. The events are independent, so multiply: 1/4 × 1/2 = 1/8.
Question 4
Sam flips a coin 10 times and gets 7 heads. What does this show?
- The next flip is more likely to be tails
- The coin will land heads 70% of the time from now on
- Experimental results can differ from the theoretical probability
- The theoretical probability of heads is 7/10
Experimental results can differ from the theoretical probability
Hint: Theoretical P(heads) is still 1/2. Ten flips is a small experiment, so 7 heads isn't surprising, and the coin has no memory.
Question 5
You roll a standard die (1 to 6) and spin a spinner with 4 equal sections. How many different outcomes are possible?
answer box
24
Hint: Each of the 6 results of the first event can pair with each of the 4 results of the second: 6 × 4 = 24 outcomes. A tree diagram or table shows them all.
Question 6
Suppose you flip a coin and roll a standard die (1 to 6), and repeat this 240 times. About how many times would you expect to get tails and a number greater than 4?
answer box
40
Hint: P(tails and a number greater than 4) = 1/2 × 2/6 = 1/6. Expected: 1/6 × 240 = 40 times.