To find the probability that the die lands on 4 and the card drawn from a standard deck of cards is a heart, we first determine the probabilities of each individual event.
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Probability of rolling a 4 on a die: A standard die has 6 faces, each representing a different number (1 through 6). The probability of rolling a specific number (in this case, 4) is: \[ P(\text{rolling a 4}) = \frac{1}{6} \]
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Probability of drawing a heart from a deck of cards: A standard deck contains 52 cards, of which 13 are hearts. The probability of drawing a heart is: \[ P(\text{drawing a heart}) = \frac{13}{52} = \frac{1}{4} \]
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Calculating the combined probability: Since the dice roll and the card draw are independent events, we can multiply their probabilities to find the combined probability: \[ P(\text{rolling a 4 and drawing a heart}) = P(\text{rolling a 4}) \times P(\text{drawing a heart}) = \frac{1}{6} \times \frac{1}{4} \]
Calculating the product: \[ P(\text{rolling a 4 and drawing a heart}) = \frac{1}{6} \times \frac{1}{4} = \frac{1}{24} \]
Thus, the probability that the die lands on 4 and the card drawn is a heart is \(\frac{1}{24}\).