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**Statistics solution**

- From Mathematics, Statistics

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1. –/3 points

A standard deck of playing cards has 52 cards, consisting of 13 "ranks" (2, 3, 4, 5, 6, 7, 8, 9, 10,

jack, queen, king, ace) of each of the 4 "suits" (hearts, diamonds, spades, clubs). In the game of

poker each player is dealt a set of cards which is called the players "hand". If five cards are dealt to

a poker player it is called a "5card

poker hand".

Pete is a poker player. He's just been dealt a 5card

poker hand. Here are some possible events.

A = He has 3 queens.

B = He has 4 kings.

C = He has a full house (a hand with three cards of one rank and two of a second rank).

D = He has at least one spade.

E = He has 2 jacks.

Answer the following questions.

Which of the following sets of events are mutually exclusive? (Select all that apply.)

events A and B

events A and C

events B and D

events A and E

None of these, 5card

poker hands can never have mutually exclusive events.

Which of the following sets of events are independent? (Select all that apply.)

events A and B

events A and C

events B and D

events A and E

None of these, 5card

poker hands can never have independent events.

Which of the following sets of events are neither mutually exclusive nor independent? (Select

all that apply.)

events A and B

events A and C

events B and D

events A and E

None of these, 5card

poker hands can never have events which are neither mutually

exclusive nor independent.

2017/4/7 Section 5.6 (Part A) [43 points]

At the scene of a crime, the police have found a blood stain, a footprint, and some threads from a

fabric. All are presumed to have been left by the person who committed the crime.

After analyzing the evidence it is found that:

The blood type is a type found in only 10% of the population.

The footprint is a size 13 men's shoe and only 10% of the population wears that shoe size.

Only 30% of the population owns clothing made from a fabric that matches the thread samples

found at the scene.

The police have a suspect who matches all of the criteria. He has the same blood type, the same

shoe size, and owns clothing matching the threads found at the scene of the crime.

While this is only circumstantial evidence, what is the probability that a random person would match

all of these characteristics if the three characteristics are assumed to be independent of each other?

(Give your answer correct to four decimal places.)

3. –/2 points

Suppose that 15% of a population is redheaded,

and 15% of the same population is lefthanded.

If

these two traits are independent of each other, what is the probability that a randomly selected

person from this population would be both redheaded

and lefthanded?

4. –/2 points

Four salesmen play "odd man out" to see who pays for lunch. They each flip a coin, and if there is a

salesman whose coin doesn't match the others he pays for lunch. To clarify, the "odd man" must get

heads while the other three get tails OR he must get tails while the other three get heads. Of course,

since it is possible for two men get heads and two men get tails, not all flips will result in finding an

"odd man". If this occurs the salesmen would be forced to flip again.

What is the probability that there is an "odd man" the first time they flip?

2

Kim and Susan are playing a tennis match where the winner must win 2 sets in order to win the

match.

For each set the probability that Kim wins is 0.59. The probability of Kim winning the set is not

affected by who has won any previous sets.

(a) What is the probability that Kim wins the match?

(b) What is the probability that Kim wins the match in exactly 2 sets (i.e. only 2 sets are

played and Kim is the one who ends up winning)?

(c) What is the probability that 3 sets are played?

6. –/12 points

Suppose that two teams called the Hogs and the Grunts are in a playoff series where the first team

to win 2 games wins the series. For each game they play, the probability that the Hogs win is 0.52

and the probability the Grunts win is 0.48.

(a) What is the probability that the Hogs win the series in exactly 2 games (i.e. only 2 games

are required to finish the series and the Hogs are the ones that win)?

(b) What is the probability that the Grunts win the series in exactly 2 games?

(c) What is the probability that the Hogs win the series in exactly 3 games?

(d) What is the probability that the Grunts win the series in exactly 3 games?

(e) What is the probability that the Hogs win the series (i.e. the Hogs win but we don't care

how many games are required)?

(f) What is the probability that the Grunts win the series?

7. –/16 points

Suppose that two teams called the Bears and Wildcats are in a playoff series where the first team to

win 3 games wins the series. For each game they play, the probability that the Bears win is 0.63 and

the probability the Wildcats win is 0.37.

(a) What is the probability that the Bears win the series in exactly 3 games (i.e. only 3

games are required to finish the series and the Bears are the ones that win)?

(b) What is the probability that the Wildcats win the series in exactly 3 games?

(c) What is the probability that the Bears win the series in exactly 4 games?

(d) What is the probability that the Wildcats win the series in exactly 4 games?

(e) What is the probability that the Bears win the series in exactly 5 games?

(f) What is the probability that the Wildcats win the series in exactly 5 games?

(g) What is the probability that the Bears win the series (i.e. the Bears win but we don't care

how many games are required)?

(h) What is the probability that the Wildcats win the series?

**Statistics solution**

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- Submitted On 07 Apr, 2017 07:32:01

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