If you roll one fair six-sided die, what is the probability that the

hi i thought or means you have to add the probabilty of each?

The probability of getting a number less than 4 is 1/2 (1, 2, or 3), and the probability of getting an even number is also 1/2 (2, 4, or 6). However, both of these probabilities include the number 2, which is both even and less than 4, so its probability (1/6) gets counted twice. To avoid double counting, we subtract the probability of rolling a 2:

1/2 + 1/2 - 1/6 = 5/6.

You should have noticed that adding 1/2 + 1/2 gives 1, which implies a 100% probability, and that's clearly not correct for this event.

Alternatively, you could recognize that the only outcome that isn’t favorable is 5, which has a probability of 1/6. Therefore, the probability of the favorable outcomes is 1 - 1/6 = 5/6.

Or, you could list the favorable outcomes: 1, 2, 3 (numbers less than 4), and 4, 6 (even numbers). This gives a total probability of 5/6.