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Math  /  Discrete

QuestionWrite out the sample space for the given experiment. Use the letter HH to indicate heads and T for tails. 3 coins are tossed.

Studdy Solution

STEP 1

1. Each coin has two possible outcomes: Heads (H) or Tails (T).
2. The experiment involves tossing 3 coins simultaneously.
3. The sample space includes all possible outcomes of the 3 coin tosses.

STEP 2

1. Identify the number of possible outcomes for a single coin toss.
2. Determine the total number of outcomes when 3 coins are tossed.
3. List all possible combinations of outcomes for the 3 coin tosses.

STEP 3

Identify the number of possible outcomes for a single coin toss.
Each coin can result in either Heads (H) or Tails (T), so there are 2 possible outcomes per coin.

STEP 4

Determine the total number of outcomes when 3 coins are tossed.
Since each coin has 2 possible outcomes and there are 3 coins, the total number of outcomes is: 23=8 2^3 = 8

STEP 5

List all possible combinations of outcomes for the 3 coin tosses.
The sample space SS can be written as: S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} S = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \}
Solution: The sample space for the experiment of tossing 3 coins is: S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} S = \{ HHH, HHT, HTH, HTT, THH, THT, TTH, TTT \}

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