If For Two Independent Events A And B, P(A U B)=2/3 P(A)=2/5, What Is P(B)?
4/15 or 4/9 or 5/9 or 7/15?
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The answer is 4/15
P(AUB) = P(A)+P(B)
2/3 = 2/5+P(B)
P(B) = 2/3 - 2/5
P(B) = 10/15 - 6/15
P(B) = 4/15.
P(AUB) = P(A)+P(B)
2/3 = 2/5+P(B)
P(B) = 2/3 - 2/5
P(B) = 10/15 - 6/15
P(B) = 4/15.
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If A and B are independent then,
P(A U B)=P(A)+P(B)-P(A)P(B)
putting the values
2/3=2/5+P(B)-2/5P(B)
2/3-2/5=P(B)-2/5P(B)
4/15=3/5P(B)
P(B)=4/15*5/3
P(B)=4/9
P(A U B)=P(A)+P(B)-P(A)P(B)
putting the values
2/3=2/5+P(B)-2/5P(B)
2/3-2/5=P(B)-2/5P(B)
4/15=3/5P(B)
P(B)=4/15*5/3
P(B)=4/9
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