1. **Problem statement:** We are given probabilities related to the election of two members, Avantika and Jyotsna, and we need to find the probability that both are not elected together. 2. **Given:** - Probability Avantika is elected: $P(A) = 0.8$ - Probability Jyotsna is elected: $P(J) = 0.3$ - Probability at least one is elected: $P(A \cup J) = 0.9$ 3. **Formula used:** The probability of the union of two events is given by: $$P(A \cup J) = P(A) + P(J) - P(A \cap J)$$ 4. **Find the probability that both are elected together:** Rearranging the formula: $$P(A \cap J) = P(A) + P(J) - P(A \cup J)$$ Substitute the values: $$P(A \cap J) = 0.8 + 0.3 - 0.9 = 0.2$$ 5. **Find the probability that both are not elected together:** This is the complement of both being elected together: $$P(\text{not both elected}) = 1 - P(A \cap J) = 1 - 0.2 = 0.8$$ **Final answer:** The probability that both Avantika and Jyotsna are not elected together is **0.8**.