Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. Find the number of elements in the sample space whose outcomes are all possible sequences of three rolls of the die. (a) Find the probability of the event that exactly one of the colors that appears face up is red. Incorrect: Your answer is incorrect. (b) Find the probability of the event that at least one of the colors that appears face up is red

Question

Mathematics

Dangelo Blackwell

21 January, 16:13

Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. Find the number of elements in the sample space whose outcomes are all possible sequences of three rolls of the die. (a) Find the probability of the event that exactly one of the colors that appears face up is red. Incorrect: Your answer is incorrect. (b) Find the probability of the event that at least one of the colors that appears face up is red

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Emery Downs · Answer 1

Prob (Exactly one die has red) = 2/9

Prob (No die has red) = 5/9

Step-by-step explanation:

Prob (Red on a die) = 2/6 = 1/3

Prob (Blue on a die) = 2/6 = 1/3

Prob (Yellow on a die) = 2/6 = 1/3

Two die rolled : -

Prob (one die has red) =

Prob (one die has read & other die has non red, blue or yellow)

= (1/3) x (2/3) = 2/9

Prob atleast one die has red = 1 - Prob (No die has red)

= 1 - Prob (both die have non red, yellow or blue)

= 1 - [ (2/3) (2/3) ]

= 1 - 4/9 = 5/9