Question

Master Chef Alan makes a dish every day from one of his recipe books. He has written 3 books and each book contains 15 different recipes. What is the probability that he will cook 4th dish from 3rd book today?

• A. 1/15
• B. 3/45
• C. 3/13
• D. 1/45
• E. 1/3

Hint:

In probability questions, the first step is always to clearly define the sample space (the set of all possible outcomes). Then, identify the specific event (favorable outcome) you're interested in. Don't be confused by extra details; the "4th dish from the 3rd book" is just a label for one unique choice out of the total.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a basic probability problem. Probability is calculated as the ratio of the number of favorable outcomes to the total number of possible outcomes. We assume that any recipe is equally likely to be chosen.
Step 2: Key Formula or Approach:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}} \] First, we need to determine the total number of recipes Alan can choose from. Then, we identify how many of those choices match the specific outcome we are interested in.
Step 3: Detailed Explanation:
Calculate the Total Number of Possible Outcomes:
Alan has 3 books.
Each book has 15 recipes.
Total number of recipes = (Number of books) \(\times\) (Number of recipes per book)
\[ \text{Total Outcomes} = 3 \times 15 = 45 \] So, there are 45 different dishes Alan could potentially cook.
Calculate the Number of Favorable Outcomes:
The specific event we are interested in is "he will cook 4th dish from 3rd book".
This refers to one single, specific recipe.
Therefore, the number of favorable outcomes is 1.
Calculate the Probability:
\[ P(\text{4th dish from 3rd book}) = \frac{1}{45} \] Step 4: Final Answer:
The probability that he will cook the 4th dish from the 3rd book is 1/45.