Final answer:
The probability of Roger wearing either a blue tie or a blue coat is 4/7.
Step-by-step explanation:
To find the probability that Roger wears either a blue tie or a blue coat, we need to calculate the total number of favorable outcomes and the total number of possible outcomes. There are two blue ties and two blue coats, so a total of four favorable outcomes. There are a total of seven items (two blue ties, one red tie, two blue coats, and two orange coats) that Roger could wear. Therefore, the total number of possible outcomes is seven.
The probability of an event occurring is calculated by dividing the number of favorable outcomes by the number of possible outcomes. In this case, the probability that Roger wears either a blue tie or a blue coat is 4/7.