To find the difference between the experimental probability and the theoretical probability of getting three heads when tossing three coins, we'll first calculate both probabilities.
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Theoretical Probability:
- When tossing three coins, the total number of outcomes is \(2^3 = 8\) (each coin has 2 outcomes: heads or tails).
- Among these outcomes, there is only 1 outcome that results in three heads (HHH).
- Therefore, the theoretical probability \(P\) of getting three heads is:
\[ P(\text{three heads}) = \frac{1}{8} \]
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Experimental Probability:
- In this experiment, three heads occurred 40 times out of 100 trials.
- Thus, the experimental probability \(P_e\) is:
\[ P_e = \frac{40}{100} = \frac{4}{10} = \frac{2}{5} \]
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Calculate the difference:
- We need to find the difference between the experimental probability and the theoretical probability:
\[ \text{Difference} = P_e - P = \frac{2}{5} - \frac{1}{8} \]
- To subtract these fractions, we need 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:
\[ \frac{16}{40} - \frac{5}{40} = \frac{16 - 5}{40} = \frac{11}{40} \]
Thus, the difference between the experimental probability of getting three heads and its theoretical probability in simplest form is:
\[ \frac{11}{40} \]