Darrin tosses a quarter and a penny 20 times. He gets heads on both coins twice. Compare the theoretical probability of getting heads on both coins with Darrin’s experimental probability of getting heads on both coins. Why might the probabilities differ?

Answer 1

The 4 possible outcomes are HH, HT, TH, TT.
So theoretically, HH should occur 1in 4 times.
1/4 = x/20
x = 5

So why is it actually 2 in 20 when theoretically it should be 5 in 20? One reason is that theoretical probabilities gain more accuracy with larger numbers of results (e.g tossing the coins 100 times). You can likely think of some more reasons.