180 students in a tenth grade high school class take a survey about which video game consoles they own.
80 students answer that one of their consoles is a Playstation, 90 answer that one of their consoles is an
Xbox. Out of these, there are 30 who have both systems.

Let A be the event that a randomly selected student in the class has a Playstation and B be the event that
the student has an Xbox. Based on this information, answer the following questions.

What is P(A), the probability that a randomly selected student has a Playstation?

What is P(B), the probability that a randomly selected student has an Xbox?

What is P(A and B), the probability that a randomly selected student has a Playstation and an Xbox?

What is P(B A), the conditional probability that a randomly selected student has an Xbox given that he or she has a Playstation?

Is P(B|A) = P(B)? Are the events A and B independent?

P(A) = 44.44%

P(B) = 50%

P(B|A) = 37.5%

P(B|A) different from P(B).

A and B are independent.

Step-by-step explanation:

If we have a total of 180 students, and 80 of them have a Playstation, we have that P(A) = 80/180 = 0.4444 = 44.44%

If we have 90 students that have a Xbox, we have that P(B) = 90/180 = 0.5 = 50%

If we have 30 students that have both consoles, we have that P(A and B) = 30/180 = 0.1667 = 16.67%

To find P(B|A), we will find for a student that has an Xbox inside the group of students that has a Playstation, that is, we have 30 students in a total of 80 students, so P(B|A) = 30/80 = 0.375 = 37.5%

P(B|A) is different from P(B), the first is 37.5% and the second is 50%, so events A and B are independent events.

Ur answer is in attachment

need more information

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15