To find the experimental probability of getting three heads and the theoretical probability, let's calculate both.
-
Experimental Probability:
- The experiment was carried out 100 times, and three heads occurred 40 times.
- Therefore, the experimental probability \( P(E) \) of getting three heads is: \[ P(E) = \frac{\text{Number of times three heads occurred}}{\text{Total number of tosses}} = \frac{40}{100} = \frac{2}{5} \]
-
Theoretical Probability:
- When tossing three coins, the possible outcomes are:
- HHH, HHT, HTH, HHT, THH, HTT, THT, TTH, TTT
- There are a total of \( 2^3 = 8 \) possible outcomes. Only one of these outcomes is three heads (HHH).
- Therefore, the theoretical probability \( P(T) \) of getting three heads is: \[ P(T) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8} \]
- When tossing three coins, the possible outcomes are:
-
Finding the Difference:
- Now, we need to find the difference between the experimental probability and the theoretical probability: \[ \text{Difference} = P(E) - P(T) = \frac{2}{5} - \frac{1}{8} \]
- To subtract these fractions, find a common denominator. The least common multiple of 5 and 8 is 40.
- Convert each fraction: \[ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \] \[ \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40} \]
- Now subtract the fractions: \[ \text{Difference} = \frac{16}{40} - \frac{5}{40} = \frac{16 - 5}{40} = \frac{11}{40} \]
Thus, the difference between the experimental probability of getting three heads and its theoretical probability is \( \frac{11}{40} \).