Respuesta :

lizvalle

Answer:

P(A^B) = 22/15 or 1 7/15

Step-by-step explanation:

To find the P (A^B), we add the probability of events A and B.

2/3 + 4/5 = P, we need to find the LCD to add disimilar fractions

LCD is 15.

2(5)/15 +4(3)/15 = 10/15 + 12/15 = 22/15

kudzordzifrancis

Answer:

A. [tex]P(A\cap B=\frac{14}{15}[/tex]

Step-by-step explanation:

Use the formula;

[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

It was given that;

[tex]p(A)=\frac{2}{3}[/tex]

[tex]p(B)=\frac{4}{5}[/tex]

and

[tex]p(A\cup B)=\frac{8}{15}[/tex]

We substitute all these values into the formula to get;

[tex]\frac{8}{15}=\frac{2}{3}+\frac{4}{5}-P(A\cap B)[/tex]

[tex]\frac{8}{15}-\frac{2}{3}-\frac{4}{5}=-P(A\cap B)[/tex]

The least common denominator is 15

[tex]\frac{8-10-12}{15}=-P(A\cap B)[/tex]

[tex]\frac{-14}{15}=-P(A\cap B)[/tex]

Divide both sides by -1.

[tex]\frac{14}{15}=P(A\cap B)[/tex]

[tex]P(A\cap B=\frac{14}{15}[/tex]