Final answer:
Jack is eating faster than Nora, with a rate of 0.435 cookies per minute compared to Nora's 0.421. In a box of assorted cookies, there's a 40% chance a cookie contains either chocolate or nuts, and a 60% chance it contains neither. When choosing cookies, Miguel's second selection is dependent on his first, and he takes two cookies total.
Step-by-step explanation:
Comparing Eating Speeds
First, we can find the rate at which Jack and Nora are eating cookies by dividing the number of cookies they eat by the time taken. For Jack, the rate is 10 cookies / 23 minutes which is approximately 0.435 cookies per minute. For Nora, the rate is 16 cookies / 38 minutes which is approximately 0.421 cookies per minute.
Comparing these two rates, we can see that Jack's rate of 0.435 cookies per minute is faster than Nora's 0.421 cookies per minute. Therefore, Jack is eating faster than Nora.
Probability of Cookie Contents
In a box of assorted cookies, if 36 percent contain chocolate and 12 percent contain nuts, with 8 percent containing both, to find the probability of a cookie containing either chocolate or nuts, we use the formula P(C OR N) = P(C) + P(N) - P(C AND N). This results in 0.36 + 0.12 - 0.08 = 0.40, meaning there's a 40% chance a cookie contains either chocolate or nuts.
For someone who is allergic to both, the probability of a cookie not containing chocolate nor nuts is 1 - P(C OR N), which is 1 - 0.40 = 0.60 or 60%.
Cookie Selection by Miguel
Miguel's selection process involves probabilities that change after the first cookie is selected. Since the probability of selecting a specific flavor changes after one cookie is taken, the probabilities of the second selection are dependent on the first. He takes a total of two cookies.