Question

1. In a class of 22 students, 9 have a cat and 5 have a dog. There are 3 students who have a cat and a dog. What is the probability that a student chosen randomly from class has a cat or a dog? 2. In a class of 29 students, 15 are female and 8 have an A in the class. There are 11 students who are male and do not have an A in the class. What is the probability that a student chosen randomly from the class is a female who has an A?3. In a class of 18 students, 11 have a cat and 12 have a dog. There are 4 students who do not have a cat or a dog. What is the probability that a student chosen randomly from the class has a cat or a dog?4. In a class of 22 students, 5 are a female and 11 have an A in the class. There are 3 students who are female and have an A in the class. What is the probability that a student chosen randomly from the class is a male?5. In a math class with 28 students, a test was given the same day that an assingment was due. There were 19 students who passed the test and 18 students who completed the assingment. There were 6 students who failed the test and also did not complete the assingment . What is the probability that a student who did not complete the homework passed the test?6. In a class of 21 students, 7 have a brother and 6 have a sister. There are 4 students who have a brother and a sister. What is the probability that a student who has a brother also has a sister?

Answer 1

1. Let's make a diagram:

In the class, 6+3+2= 11 students have a pet, either a cat or a dog

Therefore, the probability that a student chosen randomly from class has a cat or a dog is:

`(11)/(22)\rightarrow(1)/(2)=0.5`

2. Let's take a look at the diagram of the situation:

Out of 29 students, 5 are female and have an A.

Therefore, the probability that a student chosen randomly from the class is a female who has an A is:

`(5)/(29)\rightarrow0.17`

3. Let's take a look at the diagram of the situation:

There are 18-4= 14 students with a pet, either a cat or a dog. Therefore, the probability that a student chosen randomly from the class has a cat or a dog is:

`(14)/(18)\rightarrow(7)/(9)=0.78`

4. Let's take a look at the diagram of the situation:

There are 9+8= 17 males in the class. Therefore, the probability that a student chosen randomly from the class is a male is:

`(17)/(22)=0.77`

5. Let's take a look at the diagram of the situation:

Notice that out of 28-18= 10 students that didn't complete the homework, 4 students passed the test.

Therefore, the probability that a student who did not complete the homework passed the test is:

`(4)/(10)=0.4`

6. Let's take a look at the diagram of the situation: