1. **State the problem:** We have a probability distribution for items sold by the Booster Club with some probabilities given and one missing. We need to find the missing probability and answer questions about probabilities involving chips and hot dogs. 2. **Sum of probabilities rule:** The sum of all probabilities in a distribution must equal 1. 3. **Given probabilities:** - Hot dog and drink: 0.11 - Hot dog chips & drink: missing (let's call it $p$) - Pizza, chips, & drink: 0.26 - Pizza & drink: 0.24 - Cookie: 0.14 4. **Find the missing probability $p$:** $$0.11 + p + 0.26 + 0.24 + 0.14 = 1$$ $$p = 1 - (0.11 + 0.26 + 0.24 + 0.14)$$ $$p = 1 - 0.75 = 0.25$$ 5. **Probability of selling a plate with chips:** Items with chips are Hot dog chips & drink and Pizza, chips, & drink. $$P(\text{chips}) = 0.25 + 0.26 = 0.51$$ 6. **Probability of selling a plate with a hot dog:** Items with hot dog are Hot dog and drink and Hot dog chips & drink. $$P(\text{hot dog}) = 0.11 + 0.25 = 0.36$$ 7. **Summary:** - Missing probability is 0.25. - Probability of selling a plate with chips is 0.51. - Probability of selling a plate with a hot dog is 0.36. These probabilities are found by adding the relevant probabilities from the distribution, ensuring the total sums to 1.