1. **State the problem:** We want to find the probability that a randomly chosen candy is either red or has no smile. 2. **Identify given probabilities:** From the table: - $P(\text{Red and Smile}) = 0.10$ - $P(\text{Red and No Smile}) = 0.20$ - $P(\text{Green and Smile}) = 0.30$ - $P(\text{Green and No Smile}) = 0.15$ - $P(\text{Brown and Smile}) = 0.10$ - $P(\text{Brown and No Smile}) = 0.15$ 3. **Calculate $P(\text{Red})$:** $$ P(\text{Red}) = P(\text{Red and Smile}) + P(\text{Red and No Smile}) = 0.10 + 0.20 = 0.30 $$ 4. **Calculate $P(\text{No Smile})$:** $$ P(\text{No Smile}) = P(\text{Red and No Smile}) + P(\text{Green and No Smile}) + P(\text{Brown and No Smile}) = 0.20 + 0.15 + 0.15 = 0.50 $$ 5. **Calculate $P(\text{Red and No Smile})$ (intersection):** $$ P(\text{Red and No Smile}) = 0.20 $$ 6. **Use the formula for union of two events:** $$ P(\text{Red or No Smile}) = P(\text{Red}) + P(\text{No Smile}) - P(\text{Red and No Smile}) $$ 7. **Substitute values:** $$ P(\text{Red or No Smile}) = 0.30 + 0.50 - 0.20 = 0.60 $$ 8. **Final answer:** The probability that the candy is red or has no smile is **0.60**.