Exam 5: Probability

Compute and Interpret Probabilities Using the Classical Method -A single die is rolled twice. The set of 36 equally likely outcomes is $\{ ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 2,1 )$ , $( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 5,1 )$ , $( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 6,1 ) , ( 6,2 ) , ( 6,3 ) , ( 6,4 ) , ( 6,5 ) , ( 6,6 ) \}$ . Find the probability of getting two numbers whose sum is less than 13 .

Solve Counting Problems Using the Multiplication Rule -License plates in a particular state display 2 letters followed by 4 numbers. How many different license plates can be manufactured (Repetitions are allowed.)

Use the General Addition Rule -The table lists the drinking habits of a group of college students. If a student is chosen at random, find the probability of getting someone who is a man or a non-drinker. Round your answer to three decimal places. Sex Non-drinker Regular Drinker Heavy Drinker Total Man 135 49 5 189 Woman 187 21 8 216 Total 322 70 13 405

Compute Probabilities Involving Permutations and Combinations -If you are dealt 5 cards from a shuffled deck of 52 cards, find the probability that none of the 5 cards are picture cards.

Determine the Appropriate Probability Rule to Use -Find $P ( A$ or $B )$ given that $P ( A ) = 0.7 , P ( B ) = 0.2$ , and $A$ and $B$ are mutually exclusive.

Solve Counting Problems Using Permutations -A club elects a president, vice-president, and secretary-treasurer. How many sets of officers are possible if there are 15 members and any member can be elected to each position No person can hold more than one office.

Compute Probabilities Using the General Multiplication Rule -If $\mathrm { P } ( \mathrm { A } ) = 0.45 , \mathrm { P } ( \mathrm { B } ) = 0.25$ , and $\mathrm { P } ( \mathrm { B } \mid \mathrm { A } ) = 0.45$ , are $\mathrm { A }$ and $\mathrm { B }$ independent?

Determine the Appropriate Counting Technique to Use -A poet will read 3 of her poems at an award ceremony. How many ways can she choose the 3 poems from 9 poems given that the sequence is important

Use the Addition Rule for Disjoint Events -In the game of craps, two dice are tossed and the up faces are totaled. Is the event getting a total of 9 and one of the dice showing a 6 mutually exclusive Answer Yes or No.

Use the Multiplication Rule for Independent Events -A machine has four components, $A , B , C$ , and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the other parts. Also assume that the probabilities of the individual parts working are $P ( A ) = P ( B ) = 0.94$ , $P ( C ) = 0.97$ , and $P ( D ) = 0.95$ . Find the probability that the machine works properly.

Compute At-least Probabilities -Find the probability that of 25 randomly selected students, at least two share the same birthday.

Solve Counting Problems Using Combinations -A professor wants to arrange his books on a shelf. He has 30 books and only space on the shelf for 20 of them. How many different 20-book arrangements can he make using the 30 books This is an example of a problem that can be solved using which method

Compute and Interpret Probabilities Using the Classical Method -In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. The $\mathrm { P } ($ Red $) = \frac { 18 } { 38 } \approx 0.47$ . This is an example of what type of probability?

Use the Rule of Total Probability -One of the conditions for a sample space S to be portioned into n subsets is that

Solve Counting Problems Using Combinations -In how many ways can a committee of three men and four women be formed from a group of 10 men and 10 women

Solve Counting Problems Using Combinations -To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 50 numbers (one through 50.) The order in which the selections is made does not matter. How many different selections are possible

Use the Addition Rule for Disjoint Events -The below table shows the probabilities generated by rolling one die 50 times and noting the up face. Is the event rolling an odd number and rolling a number less that or equal to two a disjoint event Answer Yes or No. Roll 1 2 3 4 5 6 Probability 0.22 0.10 0.18 0.12 0.18 0.20

Use the Addition Rule for Disjoint Events -If two events have no outcomes in common they are said to be

Compute and Interpret Probabilities Using the Classical Method -In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green. We watched a friend play roulette for two hours. In that time we noted that the wheel was spun 50 times and that out of those 50 spins black came up 22 times. Based on this data, the $\mathrm { P } ( \mathrm { black } ) = \frac { 22 } { 50 } = 0.44$ . This is an example of what type of probability?

Compute Probabilities Involving Permutations and Combinations -Six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is determined by random selection. Find the probability that (a) E will speak first (b) that $C$ will speak fifth and $B$ will speak last (c) that the students will speak in the following order: DECABF (d) that A or B will speak first.