You roll a fair die three times. What is the probability of each of the followin

Question

You roll a fair die three times. What is the probability of each of the following? a) You roll all 5's. b) You roll all odd numbers. c) None of your rolls gets a number divisible by 3. d) You roll at least one 1. e) The numbers you roll are a) P(all 5's) = (Type an integer or decimal rounded to four decimal places as needed.) b) P(all odd numbers) = (Type an integer or decimal rounded to four decimal places as needed.) c) P(none are divisible by 3) = (Type an integer or decimal rounded to four decimal places as needed.) d P(at least one 1) = (Type an integer or decimal rounded to four decimal places as needed.) e) P(not all 1's) = (Type an integer or decimal rounded to four decimal places as needed.)

Explanation / Answer

Also , please refer the attached sheet for more details.

Please note the answer in BOLD.

1. P(all 5's number) 1/216 0.00462963 1/6*1/6*1/6 Probability of getting 5's from one die 1/6 Probability of getting 5's from second die 1/6 Probability of getting 5's from third die 1/6 2.P(all odd's number) 27/216 0.125 3/6*3/6*3/6 Probability of getting odd number from one die 3/6 Probability of getting odd number from second die 3/6 Probability of getting odd number from third die 3/6 3. P(none are divisible by 3) 64/216 0.2962963 4/6*4/6*4/6 Probability of getting number not divisble by 3 from one die 4/6 Probability of getting number not divisble by 3 from second die 4/6 Probability of getting number not divisble by 3 from third die 4/6 4. P(at least one 1) 1-P(no one) 1-125/216 0.4212963 5/6*5/6*5/6 Probability of getting no 1's from first die 5/6 Probability of getting no 1's from second die 5/6 Probability of getting no 1's from third die 5/6 5. P(not all one's) 1- P(all one's) 1-1/216 215/216 0.99537 Probability of getting all one's 1/216

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