1. Determine whether each of the following represents an example of finding a probability using the...

1. Determine whether each of the following represents an example of finding a probability using the classical method, the empirical (relative frequency) method or the judgemental method.

a. A student says that they are 100% certain that they will get an A in a class at the beginning of the semester.

b. Of 350 college students polled, the probability that they are planning on going to graduate school is 0.44.

c. The probability of choosing the correct numbers in a certain lottery is 0.000024

2. About 18% of people say that winter is their favorite season. If one person is chosen at random, what is the probability that they do not say winter is their favorite season?

3. About 18% of people say that winter is their favorite season. If four people are chosen at random, what is the probability that they all say winter is their favorite season. Round your response to three decimal places.

4. Consider the following pair of events. E: A randomly chosen person was born in California. F: A different randomly chosen person was born in Washington.

Determine whether this pair of events is mutually exclusive (disjoint) or not. Explain your answer in a full sentence.

5. Consider the following pair of events. E: A randomly chosen person was born in California. F: A different randomly chosen person was born in Washington.

Determine whether this pair of events is independent or not. Explain your answer in a full sentence.

Solutions

Expert Solution

(a)

This probability is depends upon student judgement about his/her perfoamnce so it is the judgemental method of finding the probability.

(b)

It is based on poll. That is this probability depends upon the answer of students. So it is relative frequency or empirical probability.

(c)

This probability is depends upon the total number of outcomes and outcomes in favor winning lottery so it is classical probability.

Using the complement rule of probability, the probability that they do not say winter is their favorite season is

P(winter is not favorite season) =1 - P(winter is favorite season) = 1 - 0.18 = 0.82

The probability that they all say that winter is favorite season is

P(all say winter is favorite season) = 0.18* 0.18* 0.18* 0.18 = 0.00104976

No these are not disjoint events becuase these events can occur simultaneously.

Yes these are independent because occurrence of one event does not effect the occurence of other event.

orchestra answered 1 year ago

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