Question
Download Solution PDFFor two equally likely, exhaustive and independent events A and B, P(A ∩ B) is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFKey Points
1. Equally likely events are those events which have an equal probability of occurring.
- For example: When we toss an unbiased coin, the probability of getting a heads is 1/2 and the probability of getting a tails is 1/2. So, it is an equally likely event.
- If A and B are equally likely events, then P(A) = P(B)
2. Exhaustive events are a set of events in a sample space such that one of them compulsorily occurs while performing the experiment.
- For example, while tossing an unbiased coin, there are two possible outcomes - heads or tails. So, these two outcomes are exhaustive events as one of them will definitely occur while flipping the coin.
- The probability of exhaustive events is equal to 1.
3. Independent events are those events if the outcome of one event does not affect the outcome of another.
- If A and B are independent events, then P(A│B) = P(A)
- Using Multiplication rule of probability, P(A ∩ B) = P(B).P(A│B)
- P(A ∩ B) = P(B).P(A)
Important Points
For any two equally likely, exhaustive and independent events A and B.
- P(A ∩ B) = P(B).P(A)
- Since, P(A)= P(B) and P (A) + P(B) =1
- Therefore, P(A ∩ B) = 0.5 x 0.5
- P(A ∩ B) = 0.25
Thus, For any two equally likely, exhaustive and independent events A and B, P(A B) will be equal to 0.25.
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