The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
150 students in a tenth grade high school class take a survey about which video game consoles they own. 60 students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox. Out of these, there are 20 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.
a) What is P(A), the probability that a randomly selected student has a Playstation?
b) What is P(B), the probability that a randomly selected student has an XBOX?
c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?
d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?
Answer:
a) P(A) = 2/5
b) P(B) = 1/3
c) P(A and B) = 2/15
d) P(A | B) = 2/5
Step-by-step explanation:
Total no. of students = 150
No. of students having playstation = 60
No. of students having xbox = 50
No. of students who have both playstation and xbox = 20
a) What is P(A), the probability that a randomly selected student has a Playstation?
P(A) = No. of students having playstation/Total no. of students
P(A) = 60/150
P(A) = 2/5
b) What is P(B), the probability that a randomly selected student has an XBOX?
P(B) = No. of students having xbox/Total no. of students
P(B) = 50/150
P(B) = 1/3
c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?
The probability that a students has a Playstation and an Xbox is given by
P(A and B) = P(A)*P(B)
P(A and B) = (2/5)*(1/3)
P(A and B) = 2/15
d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?
The conditional probability is given by
P(A | B) = P(A and B)/P(B)
P(A | B) = (2/15)/(1/3)
P(A | B) = 2/5
Alternatively:
P(A | B) = P(A∩B)/P(B)
Where P(A∩B) is given by
P(A∩B) = No. of students who have both playstation and xbox/Total no. of students
P(A∩B) = 20/150
P(A∩B) = 2/15
P(A | B) = P(A∩B)/P(B)
P(A | B) = (2/15)/(1/3)
P(A | B) = 2/5
