Subjects probability

Coin Same Side 9Fa948

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1. **State the problem:** We toss three coins and want to find the probability that all three coins land on the same side. 2. **List all possible outcomes:** When tossing three coins, the sample space is: $$\{\text{TTT}, \text{TTH}, \text{THT}, \text{THH}, \text{HTT}, \text{HTH}, \text{HHT}, \text{HHH}\}$$ There are 8 possible outcomes in total. 3. **Identify favorable outcomes:** The coins all land on the same side if all are heads or all are tails. These outcomes are: $$\{\text{TTT}, \text{HHH}\}$$ There are 2 favorable outcomes. 4. **Use the probability formula:** $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 5. **Calculate the probability:** $$\text{Probability} = \frac{2}{8} = \frac{\cancel{2}}{\cancel{8}} = \frac{1}{4}$$ 6. **Interpretation:** The probability that all three coins land on the same side is $\frac{1}{4}$. **Final answer:** $\boxed{\frac{1}{4}}$