# What is the joint probability of this two handicap events related with Champions League today's Final?

A gambling company has these two handicap events related with today's Real Madrid versus Atlético de Madrid match:

• Atlético de Madrid +3: 1.04

Are these events dependent or independent? It doesn't seem clear to me. If they are independent I can compute the joint probability like: 1/5 * 1/1.04 But if they are not I will need the conditional probability of one of them.

• Can you explain them a bit further? Does the first mean Real to win but giving a one goal start? – mdewey May 28 '16 at 16:06
• Yes. RM -1 happens if 2-0, 3-1, 4-2 and so on (RM vs ATM). – hipoglucido May 28 '16 at 17:37

• Real Madrid win by three or more goals, with probability $$1-\frac1{1.04}\approx 0.03846$$
• Real Madrid wins by exactly two goals, with probability $$\frac{1}{5}-1+\frac1{1.04}\approx 0.16154$$
• Real Madrid wins by exactly one goal, or there is a draw or Atlético de Madrid wins, with probability $$1-\frac15 = 0.8$$
In fact the match on 28 May 2016 was a draw after $$90$$ minutes and after extra time, with Real Madrid winning on penalties, so the third possibility occurred and the $$1.04$$ bet paid off, albeit not very generously