1. A survey of all students in a school showed that 3/7 have a dog, and...

1. A survey of all students in a school showed that 3/7 have a dog, and 2/7 have a cat, and 1/7 have both a dog and a cat. If a student is selected at random, what is the probability of the student having OR a cat?

2. 40% of the students at a college live in the dorms. Of the students who live in the dorms, 10% are juniors. If a student from the college is picked at a random, what is the probability he or she is a junior who lives in the dorm?

Please explain and show steps.

Solutions

Expert Solution

Question 1

A survey of all students in the school showed that a student owns a dog with chance 3/7; owns a cat with chance 2/7 and owns both a dog and a cat, with chance 1/7.

Now, by addition rule of probability,

the chance that a randomly selected student owns a dog or a cat is

Question 2

40% of the students in a college live in dorms.

Of the students who live in dorms, 10% are juniors.

So, it is given that

Now, by definition of conditional probability, the second statement means

So, if a student is picked at random, the probability that he or she is a junior who lives in the dorm, is 0.04.

orchestra answered 1 year ago

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