Probability • Topic 2 of 5

Experimental Probability

Experimental probability comes from actually doing a trial many times and recording results: it is the number of successes divided by the number of trials. It estimates the true (theoretical) probability and gets closer to it as the number of trials grows. For example, if a spinner lands on green 18 times in 60 spins, the experimental probability of green is 18/60 = 3/10. The denominator is always the total number of trials, not the number of failures. Reduce the resulting fraction. The SAT may contrast experimental results with the theoretical value to test understanding of why they can differ.

A spinner divided into four equal sectors with a pointer arrow from the centerExperimental probabilityP = successes ÷ trials

✅ Solved examples

1. A coin lands heads 12 times in 20 flips. Experimental P(heads)?
12/20 = 3/5.
2. A spinner lands green 9 of 30 spins. Experimental P(green)?
9/30 = 3/10.
3. A die shows 6 on 5 of 40 rolls. Experimental P(6)?
5/40 = 1/8.
4. A free throw is made 15 of 25 times. Experimental P(make)?
15/25 = 3/5.

✏️ Practice — try these, take hints as needed

1. A coin lands tails 8 of 16 flips. Experimental P(tails)?
Successes over trials.
8/16.
Reduce.
1/2.
2. A spinner lands red 6 of 24 spins. Experimental P(red)?
6/24.
Reduce.
—
1/4.
3. A die shows even 10 of 30 rolls. Experimental P(even)?
10/30.
Reduce.
—
1/3.
4. A dart hits the target 14 of 35 throws. Experimental P(hit)?
14/35.
Reduce by 7.
—
2/5.
5. A card draw gives a heart 9 of 36 trials. Experimental P(heart)?
9/36.
Reduce.
—
1/4.

📝 Topic test — 8 questions

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