Question

6. Given two mutually excdlusive events 4 and B for which PlA)-027 and P(B) 0.46, find (e) P(An B); (f) P(A'n B); (g) P(A'n B); (h) P(A'uB). (c) P(AuB); (d) P(An B); (Hint: Draw a Venn diagram and fill in the probabilities associated with the various regions.)

Answer 1

Solution : ( a )

$\mathrm{P(A')= 1 - P(A) = 1 - 0.27 = 0.73}$

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Solution : ( b )

$\mathrm{P(B')= 1 - P(B) = 1 - 0.46 = 0.54}$

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Solution : ( c )

$\mathrm{P(A \cup B) = P(A)+P(B)-P(A \cap B)=0.27+0.46-0=0.73}$

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Solution : ( d )

$\mathrm{P(A\cap B)=0}$

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Solution : ( e )

$\mathrm{P(A\cap B')=P(A)=0.27}$

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Solution : ( f )

$\mathrm{P(A'\cap B)=P(B)=0.46}$

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Solution : ( g )

$\mathrm{P(A'\cap B') = 1-(P(A)+P(B))=1-(0.27+0.46)}=1-(0.73)=0.27$

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Solution : ( h )

$\mathrm{P(A'\cup B')=P(A')+P(B')-P(A'\cap B')= 0.73+0.54-0.27=1}$