A high school janitor has 140 keys on his key chain. Of these 140 keys, 100 open classroom doors, 80 open the
door to the teachers' lounge, and 60 open classroom doors and the teachers' lounge.

A high school janitor has 140 keys on his key chain. Of these 140 keys, 100 open classroom doors, 80 open the door to the teachers' lounge, and 60 open classroom doors and the teachers' lounge. Using this information, answer each of the following questions.

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.

1. What is P(C), the probability that a key opens a classroom?

2. What is P(T), the probability that a key opens the teachers' lounge?

3. What is P(C and T), the probability that a key opens a classroom and the teachers' lounge?

4. What is P(C or T), the probability that a key opens a classroom or the teachers' lounge?

Source:

Question that can be found at chegg dot com

Step-by-step explanation:

1. Let's review the information given to us to answer the problem correctly:

Number of keys the high-school janitor has = 140

Number of keys that open classroom doors = 100

Number of keys that open teachers' lounge = 80

Number of keys that open both = 60

2. What is P(C), the probability that a key opens a classroom?

Let's recall the formula of probability:

Probability = Number of favorable outcomes/Total of possible outcomes

Substituting with the real given values:

P(C) = 100/140 = 5/7 (Dividing by 20 numerator and denominator)

P(C) = 5/7

3. What is P(T), the probability that a key opens the teachers' lounge?

Substituting with the real given values:

P(T) = 80/140 = 4/7 (Dividing by 20 numerator and denominator)

P(T) = 4/7

4. What is P(C and T), the probability that a key opens a classroom and the teachers' lounge?

Substituting with the real given values:

P(C and T) = 60/140 = 3/7 (Dividing by 20 numerator and denominator)

P(C and T) = 3/7

5. What is P(C or T), the probability that a key opens a classroom or the teachers' lounge?

P(C or T) = P(C) + P(T) - P(C and T)

Substituting with the real given values:

P(C or T) = 5/7 + 4/7 - 3/7

P(C or T) = 6/7