From the given data, we have:
| x | 2 | 3 | 4 | 5 | 6 |
| --- | --- | --- | --- | --- | --- |
| p(x) | | | | | |
We need to find the value of p(x > 3).
We know that the sum of all the probabilities is equal to 1. So, we can find the missing probability by subtracting the sum of the probabilities we know from 1.
p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) = 1
We don't know the value of p(x = 2), so we can't directly calculate p(x > 3). But we can find p(x ≤ 3) and subtract it from 1 to get p(x > 3).
p(x ≤ 3) = p(x = 2) + p(x = 3)
To find p(x = 2), we can use the fact that the sum of all the probabilities is 1:
p(x = 2) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6))
Now we can substitute this into the equation for p(x ≤ 3) and solve:
p(x ≤ 3) = p(x = 2) + p(x = 3)
p(x ≤ 3) = 1 - (p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6)) + p(x = 3)
p(x ≤ 3) = 1 - (p(x = 4) + p(x = 5) + p(x = 6))
Finally, we can subtract p(x ≤ 3) from 1 to get p(x > 3):
p(x > 3) = 1 - p(x ≤ 3)
p(x > 3) = 1 - (1 - (p(x = 4) + p(x = 5) + p(x = 6)))
p(x > 3) = p(x = 4) + p(x = 5) + p(x = 6)
Therefore, the value of p(x > 3) is the sum of the probabilities for x = 4, 5, and 6.