Let S and T are two events difined on a sample space with probabilities `P(S)=0.5,P(T)=069,P(S//T)=0.5` Events S and T are

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Let S and T are two events difined on a sample space with probabilities
`P(S)=0.5,P(T)=069,P(S//T)=0.5`
Events S and T are
A. mutually exclusive
B. independent
C. Mutually exclusive and independent
D. neither mutually exclusive nor independent


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Correct Answer - B
`P(S//T)=(P(SnnT))/(P(T))`
`or 0.5=(P(SnnT))/(0.69)`
` or 0.5=(P(SnnT))/(0.69)`
`or P(SnnT)=0.5xx0.69=P(S)P(T)`
Therefore, S and T are independent.
`thereforeP(Aand T)=P(S)P(T)`
` =0.69xx0.5=0.345`
`P(SorT)=P(S)+P(T) -P(SnnT)`
`=0.5+0.69-0.345 =08450`

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