Question 1192542: following data is given
GOAL 0 1 2 3 4 5 >5
p(X=x) 0.05 0.2 0.15 0.15 0.3 0.05 0.1
find the probability that there would be total 5 goals in 2 matches?
Found 2 solutions by CPhill, ikleyn:
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **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.**
Answer by ikleyn(52787)  (Show Source):
You can put this solution on YOUR website! .
GOAL 0 1 2 3 4 5 > 5
p(X=x) 0.05 0.2 0.15 0.15 0.3 0.05 0.1
find the probability that there would be total 5 goals in 2 matches?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
P (5 goals in 2 matches) = 0.05*0.05 + 0.2*0.3 + 0.15*0.15 + 0.15*0.15 + 0.3*0.2 + 0.05*0.05 = 0.17.
ANSWER. The probability that there would be a total of 5 goals in 2 matches is 0.17, precisely (not approximately).
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