The probability or the chance of an event to happen is the number of favored outcomes over the number of possible outcomes.
Since we have a spinner divided into 18 equal sections, we have 18 possible outcomes in total. This will be our denominator.
For the first event, it asked us the probability of landing on an even number OR a multiple of 3.
From numbers 1 - 18, there are 9 even numbers (2,4,6,8,10,12,14,16,18) and 6 mutiples of 3 (3,6,9,12,15,18). The union or the combination of these sets will be (2,3,4,6,8,9,10,12,14,15,16,18). In these set, there are 12 elements. Therefore, the P(1) = 12/18 or 2/3.
For the second event, it asked us the probability of landing on an odd number OR a number between 4 and 15.
There are 9 odd numbers from 1-18. These are 1,3,5,7,9,11,13,15,17.
There are 10 numbers between 4 and 15. These are 5,6,7,8,9,10,11,12,13,14. In these two scenarios, we have 5 common numbers. These are 5,7,9,11,13.
So, there are 19 - 5 = 14 outcomes that are odd or a number between 4 and 15 and these are (1,3,5,6,7,8,9,10,11,12,13,14,15,17). Therefore, the P(option 2) = 14/18 or 7/9.