Question 1192542
**1. Define the Probability Distribution**

* We are given the probability distribution of goals scored in a single match:

| Goals (X) | 0 | 1 | 2 | 3 | 4 | 5 | >5 |
|---|---|---|---|---|---|---|---|
| P(X=x) | 0.05 | 0.2 | 0.15 | 0.15 | 0.3 | 0.05 | 0.1 |

**2. Calculate the Probability of a Total of 5 Goals in 2 Matches**

* To find the probability of a total of 5 goals in 2 matches, we need to consider all possible combinations of goals scored in each match that sum up to 5.

* **Possible Combinations:**
    * Match 1: 0 goals, Match 2: 5 goals
    * Match 1: 1 goal, Match 2: 4 goals
    * Match 1: 2 goals, Match 2: 3 goals
    * Match 1: 3 goals, Match 2: 2 goals
    * Match 1: 4 goals, Match 2: 1 goal
    * Match 1: 5 goals, Match 2: 0 goals

* **Calculate the Probability for Each Combination:**
    * For example, the probability of 0 goals in the first match and 5 goals in the second match is: 
        P(0 goals) * P(5 goals) = 0.05 * 0.05 = 0.0025

* **Calculate the Total Probability:**
    * Sum the probabilities of all possible combinations:
        P(Total 5 goals) = 
            P(0,5) + P(1,4) + P(2,3) + P(3,2) + P(4,1) + P(5,0) 
        = 0.05*0.05 + 0.2*0.3 + 0.15*0.15 + 0.15*0.15 + 0.3*0.2 + 0.05*0.05 
        = 0.0025 + 0.06 + 0.0225 + 0.0225 + 0.06 + 0.0025 
        = **0.16999999999999998** 

**Therefore, the probability that there would be a total of 5 goals in 2 matches is approximately 0.17.**