Coaching Centre
Experimental probability
Relative frequency from experiments and surveys, using it to estimate probability, and expected numbers of outcomes.
Relative frequency
A drawing pin is dropped $50$ times and lands point up $18$ times. Estimate $P(\text{point up})$.
Expected number
A die is rolled $300$ times. How many sixes would you expect?
A pin lands point up $18$ times in $50$ drops. Find the relative frequency (decimal).
$18 \div 50$.
A die is rolled $300$ times. How many sixes are expected?
$\tfrac{1}{6} \times 300$.
A coin is tossed $400$ times. How many heads are expected?
$\tfrac{1}{2} \times 400$.
In a survey, $30$ of $200$ students walk to school. Estimate $P(\text{walks})$ as a decimal.
$30 \div 200$.
Using that estimate, how many of $1000$ students would you expect to walk?
$0.15 \times 1000$.
Which experiment gives the most reliable estimate?
More trials, better estimate.
A die is rolled $12$ times with no six. This shows:
Small samples vary a lot.
A spinner lands on red $40$ times in $100$ spins. Estimate $P(\text{red})$.
$40 \div 100$.
New numbers every time. Keep going until you get five in a row.