Respuesta :

Answer:  

A)[tex]P(A\cap B)=\frac{1}{3}[/tex]

B)[tex]P(A)=\frac{1}{3}[/tex]

C)[tex]P(A\mid B)=\frac{1}{2}[/tex]

D)[tex]P(B)=\frac{2}{3}[/tex]

Step-by-step explanation:

As shown in Venn diagram :

We can see that there are two outcomes that comes in the intersection part of A and B i.e. 1 and 2.

Total number of outcomes =6

So, [tex]P(A\cap B)=\frac{2}{6}=\frac{1}{3}[/tex]

Next, As we can see that there are only two outcomes in the part of A i.e.

[tex]P(A)=\frac{3}{6}=\frac{1}{3}[/tex]

Now, we have to find [tex]P(A\mid B)[/tex]

AS we know the formula for "Conditional Probability":

[tex]PA\mid B)=\frac{P(A\cap B)}{P(B)}\\\\PA\mid B)=\frac{\frac{2}{6}}{\frac{4}{6}}\\\\PA\mid B)=\frac{2}{4}=\frac{1}{2}[/tex]

Now, lat but not the least we will find P(B), as there are 4 outcomes we can see in the section of B i.e. 3, 4, 5, 6.

[tex]P(B)=\frac{4}{6}=\frac{2}{3}[/tex]

Hence,

A)[tex]P(A\cap B)=\frac{1}{3}[/tex]

B)[tex]P(A)=\frac{1}{3}[/tex]

C)[tex]P(A\mid B)=\frac{1}{2}[/tex]

D)[tex]P(B)=\frac{2}{3}[/tex]

The probability is the ratio of the favorable event to the total number of events. Then the probabilities are as follow;

1.  P(A∩B) = 1/3

2.  P(A) = 1/3

3.  P(A|B) = 1/2

4.  P(B) = 2/3

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

The Venn diagram shows the results of two events resulting from rolling a number cube.

Total events = 6 {1, 2, 3, 4, 5, 6}

1.  The probability of (A∩B) will be

Favorable outcomes = 2 {1, 2}

[tex]\rm P (A \cap B) = \dfrac{2}{6} = \dfrac{1}{3}[/tex]

2.  The probability of (A) will be

Favorable outcomes = 2 {1, 2}

[tex]\rm P (A) = \dfrac{2}{6} = \dfrac{1}{3}[/tex]

3.  The probability of (A|B) will be

[tex]\rm P (A|B) = \dfrac{P(A \cap B)}{P(B)} \\\\\\P (A|B) = \dfrac{\frac{2}{6}}{\frac{4}{6}} \\\\\\P (A|B) = \dfrac{1}{2}[/tex]

4.  The probability of (B) will be

Favorable outcomes = 4 {3, 4, 5, 6}

[tex]\rm P (B) = \dfrac{4}{6} = \dfrac{2}{3}[/tex]

More about the probability link is given below.

https://brainly.com/question/795909

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