Respuesta :

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Assuming P(A^B) is the same as [tex]\mathbb P(A\cap B)[/tex] and P(A/B) means [tex]\mathbb P(A|B)[/tex], by the definition of conditional probability we have

[tex]\mathbb P(A|B)=\dfrac{\mathbb P(A\cap B)}{\mathbb P(B)}\iff\mathbb P(A|B)=\dfrac{\frac16}{\frac7{12}}=\dfrac27[/tex]

Answer:

Hence,

                [tex]P(A|B)=\dfrac{2}{7}[/tex]

Step-by-step explanation:

Two events are given by A and B.

Conditional probability--

It is the probability of an event given that the other event has already occurred.

We know that the conditional probability that is P(A|B) is calculated by using the formula:

[tex]P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}[/tex]

Also,

Conditional probability that is P(B|A) is calculated by using the formula:

[tex]P(B|A)=\dfrac{P(A\bigcap B)}{P(A)}[/tex]

Here we are asked to find:

                   P(A|B)

Given that:

[tex]P(B)=\dfrac{7}{12}\ and\ P(A\bigcap B)=\dfrac{1}{6}[/tex]

Hence,

[tex]P(A|B)=\dfrac{\dfrac{1}{6}}{\dfrac{7}{12}}\\\\i.e.\\\\P(A|B)=\dfrac{1\times 12}{7\times 6}\\\\i.e.\\\\P(A|B)=\dfrac{2}{7}[/tex]

 

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