If the probability that Ronaldo will score at least 3 goals in the mat...
Given the following probabilities:
- Probability of Ronaldo scoring at least 3 goals: 0.59
- Probability of Ronaldo's team winning the match: 0.73
We are asked to find the greatest probability where Ronaldo does not score at least 3 goals and his team does not win the match.
To solve this, we can approach it as a dependent probability problem. The outcome of Ronaldo's team winning the match depends on the number of goals Ronaldo scores.
To determine the greatest probability where neither event occurs, we can consider the complements of each event.
Let's represent the event of Ronaldo scoring at least 3 goals as A and the event of Ronaldo's team winning the match as B.
The complement of event A is "Ronaldo does not score at least 3 goals in the match," denoted as ¬A.
The complement of event B is "Ronaldo's team does not win the match," denoted as ¬B.
Given the probabilities: P(A) = 0.59 (probability of Ronaldo scoring at least 3 goals) P(B) = 0.73 (probability of Ronaldo's team winning the match)
We can calculate the complement probabilities: P(¬A) = 1 - P(A) = 1 - 0.59 = 0.41 P(¬B) = 1 - P(B) = 1 - 0.73 = 0.27
The greatest probability where neither event occurs is the probability of the intersection of the complement events, P(¬A and ¬B).
Therefore, the maximum probability where neither event occurs is 0.27.
Hence, the correct answer is option B.