1. **Problem Statement:** Three girls Jane, Alice, and Maxine complete a crossword puzzle. The probabilities of each getting it correct are Jane: $\frac{2}{5}$, Alice: $\frac{2}{3}$, Maxine: $\frac{3}{7}$. We are to find the probability that at least one gets it right. 2. **Formula and Rules:** The probability that at least one event occurs is given by: $$P(\text{at least one}) = 1 - P(\text{none})$$ where $P(\text{none})$ is the probability that none get it right. 3. **Calculate $P(\text{none})$:** - Probability Jane gets it wrong: $1 - \frac{2}{5} = \frac{3}{5}$ - Probability Alice gets it wrong: $1 - \frac{2}{3} = \frac{1}{3}$ - Probability Maxine gets it wrong: $1 - \frac{3}{7} = \frac{4}{7}$ Since these are independent events, multiply: $$P(\text{none}) = \frac{3}{5} \times \frac{1}{3} \times \frac{4}{7} = \frac{3 \times 1 \times 4}{5 \times 3 \times 7} = \frac{12}{105} = \frac{4}{35}$$ 4. **Calculate $P(\text{at least one})$:** $$P(\text{at least one}) = 1 - \frac{4}{35} = \frac{31}{35}$$ 5. **Explanation:** This means there is a high chance ($\frac{31}{35}$) that at least one of the three girls gets the crossword puzzle correct. Final answer: $\boxed{\frac{31}{35}}$