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For two events A and B, P(A ∪ B) = P(A) + P(A) only when
- a)A and B are equally likely events
- b)A and B are exhaustive events
- c)A and B are mutually independent
- d)A and B are mutually exclusive
Correct answer is option 'D'. Can you explain this answer?
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For two events A and B, P(A ∪ B) = P(A) + P(A) only whena)A and ...
Mutually Exclusive Events
Mutually exclusive events are events that cannot occur at the same time. For example, if we toss a coin, the events of getting a head or a tail are mutually exclusive. It is impossible to get both at the same time.
Formula for Mutually Exclusive Events
The formula for probability of mutually exclusive events is:
P(A B) = P(A) + P(B)
This is because if events A and B are mutually exclusive, then we can add the probabilities of each event to get the probability of either event occurring.
Why Option D is Correct
Option D states that events A and B are mutually exclusive. Therefore, the formula for probability of mutually exclusive events applies:
P(A B) = P(A) + P(B)
However, since events A and B are mutually exclusive, P(B) = 0. Therefore, the formula simplifies to:
P(A B) = P(A)
So, the statement P(A B) = P(A) is true only when events A and B are mutually exclusive.
Mutually exclusive events are events that cannot occur at the same time. For example, if we toss a coin, the events of getting a head or a tail are mutually exclusive. It is impossible to get both at the same time.
Formula for Mutually Exclusive Events
The formula for probability of mutually exclusive events is:
P(A B) = P(A) + P(B)
This is because if events A and B are mutually exclusive, then we can add the probabilities of each event to get the probability of either event occurring.
Why Option D is Correct
Option D states that events A and B are mutually exclusive. Therefore, the formula for probability of mutually exclusive events applies:
P(A B) = P(A) + P(B)
However, since events A and B are mutually exclusive, P(B) = 0. Therefore, the formula simplifies to:
P(A B) = P(A)
So, the statement P(A B) = P(A) is true only when events A and B are mutually exclusive.
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Community Answer
For two events A and B, P(A ∪ B) = P(A) + P(A) only whena)A and ...
Events A and B don't have a single common element [ are mutually exclusive] hence intersection of events A and B = 0 therefore union of events A and B = P(A) + P (B).
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For two events A and B, P(A ∪ B) = P(A) + P(A) only whena)A and B are equally likely eventsb)A and B are exhaustive eventsc)A and B are mutually independentd)A and B are mutually exclusiveCorrect answer is option 'D'. Can you explain this answer?
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