## A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample

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A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?━━━━━━━━━━━━━━━━━━━━━━━━━

➡️Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.➡️The problem can be solved by dividing it into 3 cases➡️Case 1: The outcome is Head and the corresponding number on the die shows Odd number➡️Total number of sample space = (1 × 3) = 3Total number of sample space = (1 × 3) = 3Sample space SHO = {(H,1), (H,3), (H,5)}➡️Case 2: The outcome is Head and the corresponding number on the die shows Even number➡️Total number of sample space = (1 × 3 × 6) = 18➡️SHE={(H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H, 4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6)}➡️Case 3: The outcome is Tail➡️Total number of sample space=1➡️Sample space ST = {(T)}➡️The overall sample spaces➡️S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6),(T)}━━━━━━━━━━━━━━━━━━━━━━━━━Answer:A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?

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ANSWER

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➡️Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.

➡️Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

➡️The problem can be solved by dividing it into 3 cases

➡️Case 1: The outcome is Head and the corresponding number on the die shows Odd number

➡️Total number of sample space = (1 × 3) = 3

Total number of sample space = (1 × 3) = 3Sample space SHO = {(H,1), (H,3), (H,5)}

➡️Case 2: The outcome is Head and the corresponding number on the die shows Even number

➡️Total number of sample space = (1 × 3 × 6) = 18

➡️SHE={(H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H, 4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6)}

➡️Case 3: The outcome is Tail

➡️Total number of sample space=1

➡️Sample space ST = {(T)}

➡️The overall sample spaces

➡️S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),

S={(H,1),(H,3),(H,5), (H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H,4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6),(T)}

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