Official Solution: A bakery sells cookies in four flavors: lemon, chocolate, vanilla, and strawberry. Cookies are made in three shapes: star, heart, and circle. Cookies also come in two sizes: small and large. The bakery has an equal number of cookies of each possible flavor-shape-size combination. Nina wants a large, star-shaped, lemon cookie. If her friend randomly picks one cookie from the display, what is the probability that the cookie picked has at least two of the three features Nina wants?A. \(\frac{1}{24}\)
B. \(\frac{1}{4}\)
C. \(\frac{7}{24}\)
D. \(\frac{3}{8}\)
E. \(\frac{17}{24}\)
Total equally likely cookies = 4 * 3 * 2 = 24.
Nina wants lemon, star, large.
Count cookies that match at least two of these:
All three features:
• 1 cookie (large, star-shaped, lemon cookie).
Exactly two features:
• Star and large but not lemon: 3 cookies (chocolate, vanilla, or strawberry.).
• Lemon and large but not star: 2 cookies (heart, or circle.).
• Lemon and star but not large: 1 cookie (small).
So exactly two = 3 + 2 + 1 = 6.
At least two = 6 + 1 = 7.
Probability \(= \frac{7}{24}\).
Answer: C