Coaching Centre
Experimental probability
Relative frequency from experiments and surveys, expected number of outcomes, and comparing experimental and theoretical probability.
Relative frequency
Real results bounce around 0.5 for small numbers of tosses, then settle near the dashed line as the number of trials grows.
A coin is tossed $50$ times and lands heads $28$ times. Find the relative frequency of heads.
A spinner landed on red $45$ times in $150$ spins. How many reds would you expect in $400$ spins?
$28$ heads in $50$ tosses. Relative frequency of heads?
$28 \div 50$.
Red $45$ times in $150$ spins. Expected reds in $400$ spins?
$0.3 \times 400$.
A fair die is rolled $60$ times. How many sixes would you expect?
$\tfrac{1}{6} \times 60$.
A fair coin is tossed $200$ times. Expected heads?
$0.5 \times 200$.
In a survey of $80$ students, $12$ walk to school. Relative frequency of walking?
$12 \div 80$.
Using that survey, how many of $300$ students would you expect to walk?
$0.15 \times 300$.
Which gives the most reliable estimate of a probability?
More trials, better estimate.
A die gave $15$ sixes in $60$ rolls. This suggests:
Expected $10$; $15$ is high but not proof with only $60$ rolls.
New numbers every time. Keep going until you get five in a row.