1. **State the problem:** We want to find the odds against tossing two tails when tossing two coins. 2. **Understand the sample space:** When tossing two coins, each coin can be Heads (H) or Tails (T). The possible outcomes are: HH, HT, TH, TT. 3. **Identify the event:** The event "two tails" corresponds to the outcome TT. 4. **Calculate the probability of the event:** There is 1 favorable outcome (TT) out of 4 total outcomes, so the probability is $$\frac{1}{4}$$. 5. **Calculate the probability of the event not happening:** The probability of not getting two tails is $$1 - \frac{1}{4} = \frac{3}{4}$$. 6. **Calculate the odds against the event:** Odds against an event are given by the ratio of the probability of the event not happening to the probability of the event happening: $$\text{Odds against} = \frac{\text{Probability of not getting two tails}}{\text{Probability of getting two tails}} = \frac{\frac{3}{4}}{\frac{1}{4}}$$ 7. **Simplify the fraction:** $$\frac{\frac{3}{4}}{\frac{1}{4}} = \frac{3}{4} \times \frac{4}{1} = 3$$ 8. **Interpretation:** The odds against tossing two tails with two coins are 3 to 1. **Final answer:** The odds against tossing two tails are 3:1.