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Subject:Mathematics

Suppose that A and B are two non-trivial events (i.e. each event happens with non-zero probability) such that  P(A|B)=P(B|A). Which of the following is a sufficient condition for the equation above to hold?

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A.) They are mutually exclusive
B.) They are independent
C.) P(A∩B)=P(A).P(B)
D.) NA
Answer is option : A
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Subject:Mathematics

True or false, if P(A)=P(A|B), then events A  and B are independent.

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A.) true
B.) false
C.) NA
D.) NA
Answer is option : A
Subject:Mathematics

Assume that a child has an equal chance of being born on any month and of either gender (male, female). Let p be the probability that given that a family has two children and at least one of them is a girl, both are girls. Furthermore, let q be the probability that given that a family has two children and at least one of them is a girl born in April, that both are girls. Does p=q?

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A.) no
B.) yes
C.) NA
D.) NA
Answer is option : A
Subject:Mathematics

Suppose there are two types of surgeries that doctors perform. Doctor A has a higher success rate than Doctor B on the first type of surgery. Doctor A also has a higher success rate than Doctor B on the second type of surgery. Is it true that Doctor A necessarily has a higher overall success rate than Doctor B?

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A.) it must be false
B.) yes, it must be true
C.) it can be true, but not necessarily
D.) Data insufficient
Answer is option : C
Subject:Mathematics

p(a|b)=p(b|a), which of the following must be true of a and b, if p(a∩b)>0?

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A.) they are mutually exclusive
B.) they happen with equal probability
C.) they are independent
D.) p(a∩b)=p(a).p(b)
Answer is option : B
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Subject:Mathematics

Suppose you flip a fair coin 10 times. What is the probability of the last two flips both being heads if you know that the first eight flips were heads?

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A.) 0.25
B.) 0.5
C.) 0.75
D.) Data insufficient
Answer is option : A
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Subject:Mathematics

Which of the following equalities is not necessarily true if A,B are events?

 

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A.) None Of These
B.) P(A∩B)= P(A). P(B)
C.) P(A U B) = P(A) + P(B) - P(A∩B)
D.) P(A∩B)= P(A). P(B|A)
Answer is option : B
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