You roll a fair die three times. What is the probability of each of the following? a) You roll all 6's. b) You roll all even numbers. c) None of your rolls gets a number divisible by 3. d) You roll at least one 5. e) The numbers you roll are not all 5's. a) P(all 6's) =D (Type an integer or decimal rounded to four decimal places as needed) b) P(all even numbers) =D (Type an integer or decimal rounded to four decimal places as needed.) c) P(none are divisible by 3) =D (Type an integer or decimal rounded to four decimal places as needed.) d) P(at least one 5) = (Type an integer or decimal rounded to four decimal places as needed) e) P(not all 5's) -O (Type an integer or decimal rounded to four decimal places as needed.)

MATLAB: An Introduction with Applications
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**Title: Probability Calculation of Die Rolls**

**Problem Statement:**

You roll a fair die three times. What is the probability of each of the following scenarios?

**a) Probability of rolling all 6’s:**
- **P(all 6’s) =** [Enter an integer or decimal rounded to four decimal places as needed.]

**b) Probability of rolling all even numbers:**
- **P(all even numbers) =** [Enter an integer or decimal rounded to four decimal places as needed.]

**c) Probability that none of the rolls are divisible by 3:**
- **P(none are divisible by 3) =** [Enter an integer or decimal rounded to four decimal places as needed.]

**d) Probability of rolling at least one 5:**
- **P(at least one 5) =** [Enter an integer or decimal rounded to four decimal places as needed.]

**e) Probability that the numbers rolled are not all 5’s:**
- **P(not all 5’s) =** [Enter an integer or decimal rounded to four decimal places as needed.]

**Instructions:**
Enter your calculated probability value in each of the answer boxes provided.

This exercise helps in understanding the basic principles of probability with repetitive independent events, using a fair six-sided die as the context.
Transcribed Image Text:**Title: Probability Calculation of Die Rolls** **Problem Statement:** You roll a fair die three times. What is the probability of each of the following scenarios? **a) Probability of rolling all 6’s:** - **P(all 6’s) =** [Enter an integer or decimal rounded to four decimal places as needed.] **b) Probability of rolling all even numbers:** - **P(all even numbers) =** [Enter an integer or decimal rounded to four decimal places as needed.] **c) Probability that none of the rolls are divisible by 3:** - **P(none are divisible by 3) =** [Enter an integer or decimal rounded to four decimal places as needed.] **d) Probability of rolling at least one 5:** - **P(at least one 5) =** [Enter an integer or decimal rounded to four decimal places as needed.] **e) Probability that the numbers rolled are not all 5’s:** - **P(not all 5’s) =** [Enter an integer or decimal rounded to four decimal places as needed.] **Instructions:** Enter your calculated probability value in each of the answer boxes provided. This exercise helps in understanding the basic principles of probability with repetitive independent events, using a fair six-sided die as the context.
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