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The sum of probabilities of two students...

The sum of probabilities of two students getting distinction in their final examinations is 1.2.

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To determine whether the statement "The sum of probabilities of two students getting distinction in their final examinations is 1.2" is true or false, we can analyze the situation step by step. ### Step 1: Understanding Probabilities The probability of an event is a measure of the likelihood that the event will occur. The value of probability ranges from 0 to 1, where 0 indicates that the event will not occur, and 1 indicates certainty that the event will occur. ### Step 2: Sum of Probabilities For any two independent events, the sum of their probabilities can exceed 1. This is because the events are not mutually exclusive, meaning that the occurrence of one event does not affect the occurrence of the other. ### Step 3: Analyzing the Given Probabilities In this case, we are given that the sum of the probabilities of two students getting distinction is 1.2. Let's denote the probabilities of the two students getting distinction as P(A) and P(B). According to the problem: \[ P(A) + P(B) = 1.2 \] ### Step 4: Evaluating the Probabilities Since probabilities can range from 0 to 1, the maximum value for each student’s probability is 1. Therefore, if we assume: - P(A) could be 0.9 (which is a valid probability), - P(B) could be 0.3 (which is also a valid probability), Then: \[ P(A) + P(B) = 0.9 + 0.3 = 1.2 \] This shows that it is possible for the sum of the probabilities to exceed 1 when the events are independent. ### Step 5: Conclusion Since the sum of the probabilities of two independent events can exceed 1, the statement that "The sum of probabilities of two students getting distinction in their final examinations is 1.2" is true. ### Final Answer: The statement is **True**. ---

To determine whether the statement "The sum of probabilities of two students getting distinction in their final examinations is 1.2" is true or false, we can analyze the situation step by step. ### Step 1: Understanding Probabilities The probability of an event is a measure of the likelihood that the event will occur. The value of probability ranges from 0 to 1, where 0 indicates that the event will not occur, and 1 indicates certainty that the event will occur. ### Step 2: Sum of Probabilities For any two independent events, the sum of their probabilities can exceed 1. This is because the events are not mutually exclusive, meaning that the occurrence of one event does not affect the occurrence of the other. ...
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