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A box contains six red tags numbered 1 through 6, and four white tags numbered 1 through 4. One tag is drawn at random.

6.Write the sample space for this experiment.

S={R1,R2,R3,R4,R5,R6,W1,W2,W3,W4}?

Calculate the following probabilities:

7.P(red)=6/10=.68.P(even number) = 5/10=.5

9.P(red and even)= 3/10=.310.P(red or even) =8/10=.8

11.P(neither red nor even) =1-.8=.212.P(even | red) ??

13.P(red | even) =??14.P( <4 | odd) = ??

Suppose that for a group of consumers, the probability of eating pretzels is .75 and that the probability of drinking Coke is .65. Further suppose that the probability of eating pretzelsanddrinking Coke is .55. Determine if these two events areindependent.

These events are not independent.

Consider the following experiment: The letters in the word AARDVARK are printed on square pieces of tagboard (same size squares)with one letter per card. The eight letter cards are then placed in a hat, and one letter card is randomly chosen (without looking) from the hat.

16.List the sample space S of all possible outcomes.

S = {A,R,D,V,K}

17.Make a table that shows the set of outcomes (X) and the probability of each outcome:

Outcomes__A______R_______D________V__________K____ __________

P(X) .375 .25 .125 .125 .125

18.Consider the following events:

V: the letter chosen is avowel.

F: the letter chosen falls in thefirsthalf of the alphabet

(i.e., between A and M).

List the outcomes in each of the following events, and determine their probabilities:

V = {A} P(V) = .375

F = {A,D,K} P(F) =.125+.125-(.125*.125)=.234375

V or F = {A,D,K} P(V or F) = ??????

complement of F = {V,R} P(Fc) = 1-.234375=.765625

19.Determine if the events V and F are independent.

????

Age 14-17 18-24 25-34 ≥35

Male .01 .30 .12 .04

Female .01 .30 .13 .09

20.What is the probability that the student is a female?

.53

21.What is the conditional probability that the student is a female given that the student is at least 35 years old?

.09/.15=.6

22.What is the probability that the student is either a female or at least 35 years old?

???

24.If three dice are rolled, find the probability of getting triples – i.e., 1,1,1 or 2,2,2 or 3,3,3 etc.

6*6*6=216

6/216=.0277778

If I got anything wrong, can somebody point out what I did wrong and how I should approach it instead. For the question mark problems, please teach me how to do those. Thank you very much.