Subjects probability

Rock Then Scissors 727560

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1. **State the problem:** We want to find the probability that Samuel chooses Rock in Game 1 and then Scissors in Game 2. 2. **Identify the probabilities from the tree diagram:** - Probability of choosing Rock in Game 1 is 20%, or $0.20$. - Given he chose Rock in Game 1, the probability of choosing Scissors in Game 2 is 23%, or $0.23$. 3. **Use the multiplication rule for independent events:** The probability of both events happening in sequence is the product of their probabilities: $$P(\text{Rock then Scissors}) = P(\text{Rock in Game 1}) \times P(\text{Scissors in Game 2 | Rock in Game 1})$$ 4. **Calculate the probability:** $$P = 0.20 \times 0.23 = 0.046$$ 5. **Interpret the result:** The probability that Samuel chooses Rock first and then Scissors is $0.046$, or 4.6%.