Question

300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300 students, 200 have a dog, 180 have a cat, and 150 have a cat and a dog. Using this information, answer each of the following questions.
Let D be the event that a randomly selected student has a dog and C be the event that a randomly selected student has a cat.

Answer 1

This Question is not complete

Complete Question:

300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300 students, 200 have a dog, 180 have a cat, and 150 have a cat and a dog. Using this information, answer each of the following questions, Let D be the event that a randomly selected student has a dog and C be the event that a randomly selected student has a cat.

a . What is P(D), the probability that a student in the class has a dog?

b. What is P(C), the probability that a student in the class has a cat?

c. What is P(D and C), the probability that a student in the class has a dog and a cat?

d. What is P(D or C), the probability that a student in the class has a dog or a cat?

Answer:

a. 2/3

b) 3/5

c) 1/2

d) 19/ 15 = 1 4/15

Step-by-step explanation:

The formula for probability =

Number of possible outcomes ÷ Number of events.

Total number of Students = 300

Number of Students that have a dog = 200

Number of Students that have a cat = 180

Number of Students that have a dog and cat = 150

a. What is P(D), the probability that a student in the class has a dog?

In the question, the given data is interpreted as :

Number of possible outcomes = 200

Number of events = 300

P(D) = 200/300

= 2/3

Therefore, the probability that a student has a dog = 2/3

b. What is P(C), the probability that a student in the class has a cat?

In the question, the given data is interpreted as :

Number of possible outcomes = 180

Number of events = 300

P(D) = 180/300

= 3/5

Therefore, the probability that a student has a cat = 3/5

c. What is P(D and C), the probability that a student in the class has a dog and a cat?

In the question, the given data is interpreted as :

Number of possible outcomes = 150

Number of events = 300

P(D) = 150/300

= 1/2

Therefore, the probability that a student has a dog and cat = 1/2

d. What is P(D or C), the probability that a student in the class has a dog or a cat?

The is calculated as

P(D) + P(C)

In the above question,

P(D) is calculated as 2/3

P(C) is calculated as 3/5

Therfore, P(D or C), the probability that a student in the class has a dog or a cat is calculated as:

= 2/3 +3/5

= 19/15 = 1 4/15