mathwhiz9125
24.04.2020 •
Mathematics
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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Ответ:
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.
Ответ:
Ur answer is in attachment
Ответ:
Step-by-step explanation:
300