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Doing a chance experiment

Mathematics · Probability · ages 9-10

Name ______________________ Date ____________

Before starting 20 fair coin flips, Ari writes 'about 10 heads'. What does this number describe?
- A prediction made before the experiment
- Heads already recorded
- A count that every group must record after 20 flips
- Tails already recorded
A coin lands heads, tails, heads, tails, tails. Noor records 2 heads and 2 tails. Does her tally include every flip?
Circle one: True False
A coin lands flat after a flip. What are its two possible results?
- Heads or tails
- Odd or even
- Winning or losing
In a long experiment with a fair six-sided die, each number is expected to appear about equally often.
Circle one: True False
Sam rolls a fair six-sided die 30 times. He records nine 3s instead of the expected five. Which explanation fits?
- Chance can give more threes than the expected count.
- The next four rolls must all avoid 3.
- All future rolls will show 3 because it came up nine times.
A coin lands flat on all 26 recorded flips. There are 17 heads. How many tails were recorded?
Answer: ______________
Lena rolls a six-sided die 30 times and records five 6s. She says this proves the die is fair. Which explanation fits?
- Five sixes prove that every number has the same chance on every roll.
- One matching count does not prove that the die is fair.
- A fair die must give equal counts in 30 rolls.
- Five sixes prove that a 6 cannot appear on the next roll.
A class rolls a fair six-sided die 30 times. About how many times do they expect the number 5?
- 6
- 30
- 5
Leo flips a coin five times and records five heads. He says this proves the coin is unfair. Which explanation fits?
- A fair coin must alternate sides, so five heads proves it is unfair.
- Five heads can happen by chance. This does not prove unfairness.
- Five heads prove tails can never occur.
A bag has large red counters and small blue counters. Sofia closes her eyes but feels for a large counter on every draw. Does closing her eyes alone give every counter an equal chance?
Circle one: True False

Answer key

For grown-ups. Fold this page away before handing over the rest.

Doing a chance experiment W1-mt_J4j7d3iAfg-s1

A prediction made before the experiment · Ari has not flipped yet, so about 10 heads is a prediction. The recorded count will come from the actual flips.
False · There were 2 heads and 3 tails. Noor's counts total only 4, so one tail was not recorded.
Heads or tails · A coin that lands flat shows either heads or tails.
True · Each number on a fair six-sided die has the same chance. Equal expected counts do not guarantee equal recorded counts.
Chance can give more threes than the expected count. · Five is the expected count, not a required result. Nine threes can occur by chance, and later rolls do not have to balance the counts.
9 · Every recorded flip is heads or tails. Subtract heads from the total: 26 - 17 = 9 tails.
One matching count does not prove that the die is fair. · Five sixes matches the prediction for a fair die. That one matching count does not prove equal chances for all six numbers.
5 · The six numbers have equal chances. Sharing 30 equally among them gives an expected count of 30 divided by 6 = 5.
Five heads can happen by chance. This does not prove unfairness. · A fair coin can produce five heads in a row. This short streak alone does not prove whether Leo's coin is fair or unfair.
False · Sofia can select red counters by size without seeing them. Use same-size, same-shape counters and draw without choosing by feel.