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Varvara68 [4.7K]
3 years ago
9

Which of the following is not necessarily true for independent events A and B? P (A intersection B )equals P (A )P (B )P (A vert

ical line B )equals P (A )P (B vertical line A )equals P (B )P (A U B )equals P (A )plus P (B )
Mathematics
1 answer:
Sauron [17]3 years ago
6 0

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.

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Step-by-step explanation:

Complete Question

One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs  $0.91. There are 3.8 liters in one gallon.

a. How much does one gallon of gas cost in  Toronto? Round your answer to the nearest  cent.

b. Is the cost of gas greater in Buffalo or in  Toronto? How much greater?

Solution

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Cost of one gallon of gasoline in Buffalo, New York = 2.29 dollars

Cost of one liter of gasoline in Toronto, Canada = 0.91 dollars

One gallon = 3.8 liters

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