1. **State the problem:** We are given probabilities related to Rashmi and Devoleena joining a trip. - Probability Rashmi joins, $P(R) = 0.5$ - Probability Devoleena joins, $P(D) = 0.7$ - Probability at least one joins, $P(R \cup D) = 0.9$ We need to find the probability that both do not join together, i.e., $P(\text{neither } R \text{ nor } D)$. 2. **Recall the formula for union of two events:** $$ P(R \cup D) = P(R) + P(D) - P(R \cap D) $$ where $P(R \cap D)$ is the probability both join. 3. **Calculate $P(R \cap D)$:** $$ 0.9 = 0.5 + 0.7 - P(R \cap D) $$ $$ P(R \cap D) = 0.5 + 0.7 - 0.9 = 1.2 - 0.9 = 0.3 $$ 4. **Find the probability that both don't join:** This is the complement of at least one joining: $$ P(\text{neither } R \text{ nor } D) = 1 - P(R \cup D) = 1 - 0.9 = 0.1 $$ **Final answer:** The probability that both Rashmi and Devoleena do not join the trip is $0.1$.