Create a system of equations
x + y = 123
5x + y = 343
I use substitution
y = 123 - x
5x + 123 - x = 343
4x + 123 = 343
4x = 220
x = 55
Plug in
x + y = 123
55 + y = 123
y = 68
Check
5x + y = 343
5(55) + 68 = 343
275 + 68 = 343
343 = 343
Between the probability of union and intersection, it's not clear what you're supposed to compute. (I would guess it's the probability of union.) But we do know that

For parts (a) and (b), you're given everything you need to determine

.
For part (c), if

and

are mutually exclusive, then

, so

. If the given probability is

, then you can find

. But if this given probability is for the intersection, finding

is impossible.
For part (d), if

and

are independent, then

.
Answer:
1. Rolling a number less than 5
The numbers on a standard dice are 1, 2, 3, 4, 5, and 6. Therefore it is possible to roll a 6, but it is much more likely to be 1-5, simply because there are more of them.
2. Rolling a 2
Again, it is more likely that the result will be one of the other 5 numbers. But obviously a 2 is still an option, so it's not impossible.
3. Rolling a number less than 10
Every option is less than 10 so it is certain.
Answer:same2434..[-
Step-by-step explanation:25790=/,svxy