Two hockey players, Wayne and Mario, each independently take a penalty shot. Wayne has a 7/10 chance of scoring, while Mario has a 3/5 chance of scoring. What is the probability that;
a) they both miss
P(A and B) = P(A) x P(B)
The Attempt at a Solution
For this question I found out what the complements (P(not mario) and P(not Wayne)) for each were and then I used the formula for independent events [P(A and B) = P(A) x P(B)] to find my answer and the answer that I got was correct. However, I was wondering why I cannot just go:
P(both miss) = 1- P(both score)
I tried this method and the answer that came up was different than the answer that I got from my first method of trying to solve this question (using the complements). Could someone explain why I cannot use "P(both miss) = 1- P(both score)" to solve this question?