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? You roll all 5's. b) You roll all odd numbers, c) None of your rolls gets a number divisible by 2. d) You roll at least one 6. e) The numbers you roll are not all 6's. P(all 5's) = (Type an integer or decimal rounded to four decimal places as needed.) P(all odd numbers) = (Type an integer or decimal rounded to four decimal places as needed.) P(none are divisible by 2) = (Type an integer or decimal rounded to four decimal places as needed.) P(at least one 6) = (Type an integer or decimal rounded to four decimal places as needed.) P(not all 6's) = (Type an integer or decimal rounded to four decimal places as needed.)

Explanation / Answer

Rolling a die has 6 outcomes (1,2,3,4,5,6) and each outcome has the probability of 1/6.

a) You roll all 5's:- (1/6)^3=1/216.

b) You roll all odd numbers (1,3 or 5):- (1/3)^3=1/27

c) None are divisible by 2 (1,3 or 5):- (1/3)^3=1/27.

d) Atleast one 6:- 1-(5/6)^3=1-125/216=91/216.

e) Not all 6's:- (5/6)^3=125/216.

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