Question

1. Choose a student in grades 9 to 12 at random and ask if he or she is studying a language other than English.

Here is the distribution of results:

Language Spanish French German All others None
Probability 0.25 0.08 0.04 0.02 0.61

What is the conditional probability that a student is studying Spanish, given that he or she is studying some language other than English? Round your answer to 3decimal places.
________________


In a test for ESP (extrasensory perception), a subject is told that cards the experimenter can see but the subject cannot contain either a star, a circle, a wave, or asquare. As the experimenter looks at each of 20 cards in turn, the subject names the shape on the card. A subject who is just guessing has probability 0.25 of guessingcorrectly on each card.

1. The count of correct guesses in 20 cards has a binomial distribution. What are n and p?
A. n = 20 and p = 4.
B. n = 20 and p = 1/4.
C. n = 20 and p = 1/2.
D. n = 20 and p = 3/4.


2. What is the mean number of correct guesses in many repetitions of the experiment?
A. 5
B. 3.75
C. 1.9365
D. 10

3. What is the probability of exactly 5 correct guesses?
A. 0.00976
B. 5/20
C. 0.2023
D. 1

Answer 1

1. O = the student is studying some language other than English. (This event has probability P(O)=1-0.61 = 0.39)
S = the student is studying Spanish

*) SO = the probability that the student is studying a foreign language and studying Spanish. If no student studies more than one foreign language (a safeassumption, but do state it explicitly in your answer), then P(SO) = P(S) = 0.25

The sought conditional probability is P(S|O) = P(SO) / P(O) = 0.25/0.39 = 0.641

B. n = 20 and p = 1/4
mean number of correct guesses in many repetitions of the experiment = n*p = 5

the probability of exactly 5 correct guesses = 20C5*(3^15)/(4^20) = 0.2023

Answer 2

ntroduce the following events:
*) O = the student is studying some language other than English. (This event has probability P(O)=1-0.61 = 0.39

*) S = the student is studying Spanish

*) SO = the probability that the student is studying a foreign language and studying Spanish. If no student studies more than one foreign language (a safeassumption, but do state it explicitly in your answer), then P(SO) = P(S) = 0.24

The sought conditional probability is P(S|O) = P(SO) / P(O)



2)


1 = B
2 = A (20 * .25 = 5)
3 = A

(20C6) * (.25)^6 * (.75)^14 = .1686

Answer 3

Introduce the following events:
*) O = the student is studying some language other than English. (This event has probability P(O)=1-0.62 = 0.38)

*) S = the student is studying Spanish

*) SO = the probability that the student is studying a foreign language and studying Spanish. If no student studies more than one foreign language (a safeassumption, but do state it explicitly in your answer), then P(SO) = P(S) = 0.24

The sought conditional probability is P(S|O) = P(SO) / P(O)