Respuesta :
Answer:
P(C)= 3/4
P(T)= 1/2
P(C AND T)= 3/8
P(C OR T)= 7/8
Step-by-step explanation:
The value of the probability for the selection of different keys in middle school, P(C). P(T), P(C and T') and P(C or T) are 3/4,1/2,3/8 and 7/8 respectively.
What is the probability of an event?
Probability of an event is the ratio of number of favourable outcome to the total number of outcome of that event.
A middle school principal has 80 keys on her keychain to distribute to staff on the first day of school.
Of these 80 keys,
- 60 open classroom doors,
- 40 open the doors to the teachers' lounge,
- 30 open classroom doors and the teachers' lounge.
Let C be the event that a randomly selected key opens a classroom and T be the event that a randomly selected key opens the teachers' lounge.
- P(C), The probability that a key opens a classroom-
From the 80 keys, 60 open the classroom door. Thus, the probability that a key opens a classroom is,
[tex]P(C)=\dfrac{60}{80}\\P(C)=\dfrac{3}{4}[/tex]
- P(T), The probability that a key opens the teachers' lounge-
From the 80 keys, 40 open the doors to the teachers' lounge. Thus, the probability that a key opens the teachers' lounge is,
[tex]P(T)=\dfrac{40}{80}\\P(T)=\dfrac{1}{2}[/tex]
- P(C and T'), the probability that a key opens a classroom and the teachers' lounge-
From the 80 keys, 30 open classroom doors and the teachers' lounge. Thus, the probability that a key opens a classroom and the teachers' lounge
[tex]P(C\cap T)=\dfrac{30}{80}\\P(T)=\dfrac{3}{8}[/tex]
- P(C or T), the probability that a key opens a classroom or the teachers' lounge-
From 80 keys, 60 open classroom doors, 40 open the door to the teachers' lounge, and 30 open classroom doors
[tex]P(C\cup T)=P(C)+P(T)-P(C\cap T)\\P(C\cup T)=\dfrac{3}{4}+\dfrac{1}{2}-\dfrac{3}{8}\\P(C\cup T)=\dfrac{6+4-3}{8}\\P(C\cup T)=\dfrac{7}{8}[/tex]
Thus, the value of the probability for the selection of different keys in middle school, P(C). P(T), P(C and T') and P(C or T) are 3/4,1/2,3/8 and 7/8 respectively.
Learn more about the probability here;
https://brainly.com/question/24756209
