I have a car that's worth $5400 and a probability of 1/900 of being stolen

I have a watch that's worth $600 and a probability of 1/30 of being stolen.

The events of being stolen are independent.

Calculate the probabilities of all the possible scenarios of things being stolen

Answer:

Nothing Stolen(899/900 * 29/30 = 26071/27000)

Only car stolen(1/900 * 29/30= 29/27000)

Only watch stolen(899/900 * 1/30= 899/27000)

Both being stolen(1/900 * 1/30 = 1/27000)

Now calculate the EXPECTED VALUE:

For some reason I decided that I will take the independent probability of the watch being stolen independent prob of car being stolen the combined probability of both being stolen

Thus: 1/900(5400) 1/30(600) 1/27000(6000)= 26.22222222

But this is the INCORRECT answer

The CORRECT answer is taking all the conditional probabilities and adding them up. Thus,

29/27000(5400) 899/27000(600) 1/27000(6000)=26

OR

Just the independent probabilities alone 1/900(5400) 1/30(600) = 26

My question is why is the way I reasoned incorrect?

Why can the independent probabilities alone by themselves give the exact same answer as all the conditional probabilities combined?

Thank you