Francisco asks the students in his school what pets they have. He studies the events shown. - Event S : The student has a cat. - Event $$T$$ : The student has a dog. Francisco finds that the two events are independent. Select the equation that must be true for events $${S}$$ and $${T}$$.

Since, $${S}$$ and $${T}$$ are independent events. Hence, $${P}(S \cap T)={P}({S}) . {P}({T})$$ $$P(\frac{S}{T})=\frac{{P}(S \cap T}{P(T)}=\frac{{P}({S}) \cdot {P}({T})}{P(T)}=P(S)$$ And $$P(\frac{T}{S})=\frac{{P}(S \cap T}){P(S)}=\frac{{P}({S}) \cdot {P}({T})}{P(S)}=P(T)$$ Therefore the option $${P}(S \cap T)={P}({S}) . {P}({T})$$ is true.

Prephub

Francisco asks the students in his school what pets they have. He studies the events shown.

Event S : The student has a cat.
Event $T$ : The student has a dog.

Francisco finds that the two events are independent.

Select the equation that must be true for events ${S}$ and ${T}$ .

${P}(S \cap T)={P}({S}) \cdot {P}({T})$

$P(\frac{S}{T})=P(T)$

${P}(S \cup T)={P}({S}) \cdot {P}({T})$

$P(\frac{T}{S})=P(S)$

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