1. **Stating the problem:** We are given probabilities related to Raj and Rohan loving Simran. - Probability Raj loves Simran: $P(R) = 0.7$ - Probability Rohan loves Simran: $P(H) = 0.3$ - Probability at least one loves Simran: $P(R \cup H) = 0.85$ We need to find the probability that both Raj and Rohan do not love Simran simultaneously, i.e., $P(\text{neither } R \text{ nor } H) = P(R^c \cap H^c)$. 2. **Formula and rules:** Recall the formula for the union of two events: $$ P(R \cup H) = P(R) + P(H) - P(R \cap H) $$ Also, the complement rule: $$ P(R^c \cap H^c) = 1 - P(R \cup H) $$ 3. **Calculate the probability that both do not love Simran:** Using the complement rule: $$ P(R^c \cap H^c) = 1 - P(R \cup H) = 1 - 0.85 = 0.15 $$ 4. **Interpretation:** This means there is a 0.15 probability that neither Raj nor Rohan loves Simran simultaneously. **Final answer:** $$ \boxed{0.15} $$