Final answer:
Miguel took two cookies in total. The probabilities for the second cookie's flavor depend on the first selection. For the candy survey and the cookie ingredients probability, specific counts are needed to calculate the probabilities.
Step-by-step explanation:
The student's question pertains to probability, a mathematical concept involving chance. To answer the initial question, for an odd number of scoops, unless specified otherwise, there is no difference in the likelihood of getting more Chocolate or Vanilla, so the answer would likely be: c) It's the same. However, this seems unrelated to subsequent examples provided, which deal with concrete probabilities in given scenarios.
Cookie Probability
Miguel took two cookies based on the information provided. To represent Miguel's selections, we need to construct a probability tree.
- On the first pick, Miguel has a 3/10 chance of getting a chocolate cookie and a 7/10 chance for a butter cookie.
- If he picked a chocolate cookie first, the second pick would be 2/9 for chocolate and 7/9 for butter, as there is now one less chocolate and one less total cookie.
- If a butter cookie was chosen first, then he would have a 3/9 (1/3) chance for chocolate and 6/9 (2/3) for butter on the second pick.
The probabilities for the flavor of the second cookie are dependent on the first selection since picking a cookie alters the composition of the remaining cookies in the box.
Candy Survey
To determine if the mean number of pieces per package is the same between multicolored chocolates and peanut butter candies, we would conduct a statistical test such as a t-test assuming equal variances.
Cookie Ingredients Probability
a. To find the probability that a cookie contains chocolate or nuts would require information on the total number of cookies and the count of cookies with chocolate and nuts specifically.
b. Similarly, to find the probability that a cookie does not contain chocolate or nuts, we need the number of cookies without those ingredients.