To find the difference between the experimental probability of getting three heads and its theoretical probability, we can follow these steps:
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Theoretical Probability: The probability of getting three heads when tossing three coins can be calculated using the binomial probability formula. Each coin has two possible outcomes (heads or tails), so when we toss three coins, the total number of outcomes is \(2^3 = 8\). The only outcome that gives three heads is \(HHH\). Therefore, the theoretical probability \(P(T)\) of getting three heads is:
\[ P(T) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{8} \]
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Experimental Probability: The experimental probability \(P(E)\) was calculated based on the results of the experiment. It states that three heads occurred 40 times out of 100 trials. Therefore, the experimental probability is:
\[ P(E) = \frac{\text{Number of times three heads occurred}}{\text{Total number of trials}} = \frac{40}{100} = \frac{4}{10} = \frac{2}{5} \]
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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 perform this subtraction, we need a common denominator. The least common multiple of 5 and 8 is 40. Therefore:
Convert \(\frac{2}{5}\) to have a denominator of 40:
\[ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} \]
Convert \(\frac{1}{8}\) to have a denominator of 40:
\[ \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40} \]
Now we can subtract:
\[ \text{Difference} = \frac{16}{40} - \frac{5}{40} = \frac{16 - 5}{40} = \frac{11}{40} \]
Therefore, the difference between the experimental probability and the theoretical probability of getting three heads is:
\[ \boxed{\frac{11}{40}} \]