Suppose that a shop has an equal number of LED bulbs of two different types. The probability of an LED bulb lasting more than 100 hours given that it is of Type 1 is 0.7, and given that it is of Type 2 is 0.4. The probability that an LED bulb chosen uniformly at random lasts more than 100 hours is __________.

Let $T_1$ and $T_2$ denote the events that a randomly chosen bulb is of Type 1 and Type 2, respectively.

Since the shop has an equal number of bulbs of both types:

Let $E$ be the event that a bulb lasts more than 100 hours. The given conditional probabilities are:

By the Law of Total Probability:

Thus, the required probability is 0.55.