Mathematics

Problem

An urn contains 5 red and 5 blue balls. Two balls are drawn successively without replacement. Let

A

be the event "the first ball is red" and

B

be the event "the second ball is blue". Which statement is correct? a)

P(B\mid A)=P(B)

; therefore,

A \text{ and } B \text{ are independent.}

P(B\mid A)=\dfrac{4}{9}

and

P(B)=\dfrac{4}{9}

; hence,

A \text{ and } B \text{ are independent.}

P(B\mid A)\neq P(B)

, so

A \text{ and } B \text{ are not independent.}

d) The events

A

and

B

are mutually exclusive; hence

P(A\cap B)=0