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MathematicsMathematics
5 September, 19:37

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?

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Answers (1)
  1. 5 September, 20:01
    0
    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.
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