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An experiment consists of rolling a 6-sided number cube then flipping a coin. How many total outcomes are in the sample space, and what outcomes would the event “even number and heads” consist of?(1 point)

Responses

There are 12 outcomes in the sample space. The event “even number and heads” includes {2H, 4H, 6H}
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There are 12 outcomes in the sample space. The event “even number and heads” includes left brace 2 upper H comma 4 upper H comma 6 upper H right brace .

There are 6 outcomes in the sample space. The event “even number and heads” includes {1H, 2H, 3H, 4H, 5H, 6H}
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There are 6 outcomes in the sample space. The event “even number and heads” includes left brace 1 upper H comma 2 upper H comma 3 upper H comma 4 upper H comma 5 upper H comma 6 upper H right brace .

There are 6 outcomes in the sample space. The event “even number and heads” includes {2H, 4H, 6H}
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There are 6 outcomes in the sample space. The event “even number and heads” includes left brace 2 upper H comma 4 upper H comma 6 upper H right brace .

There are 12 outcomes in the sample space. The event “even number and heads” includes {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T, 6T}
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1 answer

To determine the total number of outcomes in the sample space when rolling a 6-sided number cube (die) and flipping a coin, we can analyze the situation as follows:

  1. The number cube has 6 faces, showing numbers 1 through 6.
  2. The coin has 2 sides: Heads (H) and Tails (T).

The total outcomes in the sample space can be calculated by multiplying the number of outcomes from the die by the number of outcomes from the coin:

  • Number of outcomes from the die: 6
  • Number of outcomes from the coin: 2

Total outcomes = 6 (from the die) * 2 (from the coin) = 12.

Next, we need to identify the outcomes that constitute the event “even number and heads.” The even numbers on a 6-sided die are 2, 4, and 6. When we pair these even numbers with the coin showing heads, the specific outcomes are:

  • 2H (2 and Heads)
  • 4H (4 and Heads)
  • 6H (6 and Heads)

Thus, the event “even number and heads” consists of the outcomes {2H, 4H, 6H}.

Based on this analysis, the correct response is: "There are 12 outcomes in the sample space. The event 'even number and heads' includes {2H, 4H, 6H}."