lelumorong
contestada

Two events, A and B, are associated with the following probabilities:

P(A)=23

P(A∩B)=29

If the events are independent, what is the probability of B?

P(B)= __[blank]__

Enter your answer as the fraction that correctly fills in the blank, using the / symbol, like this: 42/53

Respuesta :

gmany

If A and B are independent, then [tex]P(A\cap B)=P(A)\cdot P(B)[/tex].

We have:

[tex]P(A)=\dfrac{2}{3},\ P(A\cap B)=\dfrac{2}{9}[/tex]

Substitute:

[tex]\dfrac{2}{9}=\dfrac{2}{3}P(B)\qquad|\cdot3\\\\\dfrac{2}{3}=2P(B)\qquad|:2\\\\\dfrac{1}{3}=P(B)\\\\\boxed{P(B)=\dfrac{1}{3}}[/tex]

Otras preguntas