The probability \(P(x > 3)\) when rolling a six-sided die 10 times can be calculated as the sum of the probabilities of getting outcomes greater than 3 in each roll. Here's how you can approach it:
1. Identify the outcomes greater than 3 on a six-sided die: 4, 5, and 6.
2. Calculate the probability of getting each of these outcomes in a single roll: \(P(x = 4)\), \(P(x = 5)\), and \(P(x = 6)\).
3. Add these individual probabilities together to get the total probability of getting outcomes greater than 3 in a single roll: \(P(x = 4) + P(x = 5) + P(x = 6)\).
4. Since each roll is independent, to find the probability for 10 rolls, raise this total probability to the power of 10: \((P(x = 4) + P(x = 5) + P(x = 6))^10\).
Therefore, the correct answer would be option A: \(P(x = 4) + P(x = 5) + P(x = 6) + P(x = 7) + P(x = 8) + P(x = 9) + P(x = 10)\). This option accounts for the individual probabilities of each outcome greater than 3 in a single roll and sums them up for 10 rolls, providing the probability of getting outcomes greater than 3 in those 10 rolls.
