To determine the probability of getting a number less than 3 and a tails when rolling a six-sided die and flipping a coin, we can break down the problem as follows:
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Outcomes of the die:
- The possible outcomes of rolling a six-sided die are 1, 2, 3, 4, 5, and 6.
- The outcomes that are less than 3 are: 1 and 2. So, there are 2 favorable outcomes for the die.
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Outcomes of the coin:
- The coin can result in either heads (H) or tails (T). So there is 1 favorable outcome for getting tails.
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Total combinations:
- The total number of outcomes when rolling the die and flipping the coin is:
- 6 outcomes from the die multiplied by 2 outcomes from the coin.
- Total outcomes = 6 × 2 = 12.
- The total number of outcomes when rolling the die and flipping the coin is:
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Favorable outcomes for the event (number < 3 and tails):
- The favorable outcomes that meet our criteria (number less than 3 and tails) are:
- H 1, T 1
- H 2, T 2
- The two possibilities with Tails are:
- T 1
- T 2
- Therefore, there are 2 favorable outcomes: (T 1) and (T 2).
- The favorable outcomes that meet our criteria (number less than 3 and tails) are:
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Calculating probability:
- The probability is calculated as the number of favorable outcomes divided by the total number of outcomes: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{2}{12} = \frac{1}{6}. \]
Based on this calculation, the probability of getting a number less than 3 and a tails is \( \frac{1}{6} \).
So, the correct answer is \(\frac{1}{6}\).
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