document.write( "Question 1192542: following data is given
\n" ); document.write( "GOAL 0 1 2 3 4 5 >5
\n" ); document.write( "p(X=x) 0.05 0.2 0.15 0.15 0.3 0.05 0.1\r
\n" ); document.write( "\n" ); document.write( "find the probability that there would be total 5 goals in 2 matches? \n" ); document.write( "
Algebra.Com's Answer #848965 by CPhill(1959)\"\" \"About 
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**1. Define the Probability Distribution**\r
\n" ); document.write( "\n" ); document.write( "* We are given the probability distribution of goals scored in a single match:\r
\n" ); document.write( "\n" ); document.write( "| Goals (X) | 0 | 1 | 2 | 3 | 4 | 5 | >5 |
\n" ); document.write( "|---|---|---|---|---|---|---|---|
\n" ); document.write( "| P(X=x) | 0.05 | 0.2 | 0.15 | 0.15 | 0.3 | 0.05 | 0.1 |\r
\n" ); document.write( "\n" ); document.write( "**2. Calculate the Probability of a Total of 5 Goals in 2 Matches**\r
\n" ); document.write( "\n" ); document.write( "* 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.\r
\n" ); document.write( "\n" ); document.write( "* **Possible Combinations:**
\n" ); document.write( " * Match 1: 0 goals, Match 2: 5 goals
\n" ); document.write( " * Match 1: 1 goal, Match 2: 4 goals
\n" ); document.write( " * Match 1: 2 goals, Match 2: 3 goals
\n" ); document.write( " * Match 1: 3 goals, Match 2: 2 goals
\n" ); document.write( " * Match 1: 4 goals, Match 2: 1 goal
\n" ); document.write( " * Match 1: 5 goals, Match 2: 0 goals\r
\n" ); document.write( "\n" ); document.write( "* **Calculate the Probability for Each Combination:**
\n" ); document.write( " * For example, the probability of 0 goals in the first match and 5 goals in the second match is:
\n" ); document.write( " P(0 goals) * P(5 goals) = 0.05 * 0.05 = 0.0025\r
\n" ); document.write( "\n" ); document.write( "* **Calculate the Total Probability:**
\n" ); document.write( " * Sum the probabilities of all possible combinations:
\n" ); document.write( " P(Total 5 goals) =
\n" ); document.write( " P(0,5) + P(1,4) + P(2,3) + P(3,2) + P(4,1) + P(5,0)
\n" ); document.write( " = 0.05*0.05 + 0.2*0.3 + 0.15*0.15 + 0.15*0.15 + 0.3*0.2 + 0.05*0.05
\n" ); document.write( " = 0.0025 + 0.06 + 0.0225 + 0.0225 + 0.06 + 0.0025
\n" ); document.write( " = **0.16999999999999998** \r
\n" ); document.write( "\n" ); document.write( "**Therefore, the probability that there would be a total of 5 goals in 2 matches is approximately 0.17.**
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