Probability game with gates I am playing a game with gates and a walkway. The game is that I can only win if I get through the gate successfully. The gate works with two levers that need to be pulled. If both levers work correctly then the gate opens and you walk to the other side.

The first lever has a .01 probability of failure and the second lever has .02 probability of failure. 

I need to find the probability that when pulling both levers I successfully get through the gate. If one lever fails the gate will not open and the levers not working are statically independent. 

After looking over this problem I am having my doubts on how to approach this. I came up with four events that can happen:

A = both work

B = first fails

C = second fails

D = both fail

I need to solve for A with the other three probabilities but I am thinking that D does not matter because we only need one to fail. 

Would I have to simply use the P(B) + P(C) - P($B \cap C$) to find this answer then take the compliment to find A?
The answer is $0.99\cdot 0.98=0.9702$ because you'll only able to go to the other side if both lever works. 
Since both levers are independent, you can use the multiplication rule.
The answer is $0.99\cdot 0.98=0.9702$ because you'll only able to go to the other side if both lever works. 
Since both levers are independent, you can use the multiplication rule.