Answer:
P(A U B)=P(A)+P(B)
Step-by-step explanation:
Reading the options that we have for the answer, one of them (the first one) is the definition of being independent. A and B are independent if and only if P(A ∩ B)=P(A)*P(B).
So the first one IS necessary true for independent events and with this equation, option two and three are necessary true for independent events:
For definition of P(A | B)
P(A | B)= P(A ∩ B) / P(B)
And we replace P(A ∩ B) using the first option that we know it´s true:
P(A | B)= P(A)*P(B) / P(B)= P(A)
So P(A | B)=P(A) it´s true for A and B independent.
The same process goes to show P(B | A)=P(B)
Because of this, the only one of the options that could not be true for independent events is P(A ∪ B)=P(A) + P(B), and this happens because P(A ∩ B)=P(A)*P(B) applies but it could be different from 0 considering P(A ∪ B)=P(A) + P(B) - P(A ∩ B). We conclude this property (P(A ∪ B)=P(A) + P(B)) is not necessary true for A and B independent.
Answer:
i have no idea sorry but there are way tooooooooooo many words in this question so it doesnt really make much sence especially the bottom part if the question.
the common denominator is the number on the bottom of the fraction. in this case it would be 4 (in 3/4) and 3 (in 2/3), you have to find a number which equals the same for both! so 3 and 4 both go into 12. 3 × 4 and 4 × 3, so you common denominator is 12! but, you also have to multiple the same number up on the top number. so 3 × 3 and 2 × 4. Then you Add! but only the top numbers! you can only add/subtract fractions that have the same common denominator! your answer will end up being the improper fraction of 17/12. if you have to turn it into a decimal or make it proper, then do so ^^
to find a common denominator, you have to find the number which both numbers equally go into! so no decimals. check the times tables!
Answer:
x = 60/17, y = 24/17
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
The GCF between 54 and 27 is nine.
