Question 1: In a recipe, the probability that a randomly selected egg is fresh is 0.85. Calculate the probability that two eggs selected independently are both fresh.

Answer: 0.85 * 0.85 = 0.7225

Question 2: A baker estimates there is a 0.9 chance that a batch of dough will rise properly. What is the probability that out of 3 batches, exactly two rise properly?

Answer: 3 * (0.9)^2 * (0.1) = 3 * 0.81 * 0.1 = 0.243

Question 3: A recipe calls for 2 cups of flour, and there is a 0.7 chance that a scoop of flour is free of lumps. What's the probability that both scoops used are lump-free?

Answer: 0.7 * 0.7 = 0.49

Question 4: Construct a scenario where the probability of a successful baking attempt is 0.6, and determine the probability that at least one out of 4 attempts is successful.

Answer: 1 - P(all fail) = 1 - (0.4)^4 = 1 - 0.0256 = 0.9744

Question 5: A recipe requires 3 teaspoons of a spice, each with a probability of 0.8 of being fresh. What's the probability that all three teaspoons are fresh?

Answer: 0.8^3 = 0.512

Question 6: In a cooking experiment, the probability that a pastry turns out perfectly is 0.75. If you bake 4 pastries, what is the probability that exactly 3 turn out perfect?

Answer: 4 * (0.75)^3 * (0.25) = 4 * 0.422 * 0.25 = 0.422

Question 7: A chef estimates a 0.65 chance that a cake will be successful on the first attempt. What is the probability it takes at most two attempts for the first success?

Answer: P(success on first) + P(success on second) = 0.65 + (0.35 * 0.65) = 0.65 + 0.2275= 0.8775

Question 8: A cookie recipe has a 0.9 probability of success if the oven is preheated correctly. If a baker preheats the oven twice, what is the probability that at least one preheat is successful?

Answer: 1 - (0.1)^2 = 1 - 0.01 = 0.99

Question 9: A recipe has a 0.4 chance of failure due to missing an ingredient. What is the probability that in 5 attempts, at least one attempt fails?

Answer: 1 - (1 - 0.4)^5 = 1 - 0.6^5 = 1 - 0.07776= 0.92224

Question 10: Identify and correct the mistake: 'If the probability that a pie is perfect is 0.8, then the probability that at least one pie out of 3 is perfect is 0.8.'

Answer: Incorrect; the probability that at least one is perfect is 1 - (0.2)^3 = 1 - 0.008 = 0.992