To find the probability of landing on tails when flipping a coin and rolling an even number on a six-sided number cube simultaneously, we can break down the problem into two parts: the coin flip and the dice roll.
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Probability of flipping tails: A coin has two sides: heads (H) and tails (T). Therefore, the probability of landing on tails is: \[ P(T) = \frac{1}{2} \]
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Probability of rolling an even number: A six-sided number cube (die) has the numbers 1 through 6. The even numbers on a die are 2, 4, and 6. Thus, there are 3 favorable outcomes for rolling an even number out of a total of 6 possible outcomes. Therefore, the probability of rolling an even number is: \[ P(\text{even}) = \frac{3}{6} = \frac{1}{2} \]
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Finding the combined probability: Since the two events (flipping a coin and rolling a die) are independent, the combined probability of both events occurring is simply the product of their individual probabilities: \[ P(\text{T and even}) = P(T) \times P(\text{even}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
Thus, the probability of landing on tails and rolling an even number at the same time is: \[ \boxed{\frac{1}{4}} \]