Please give the calculation (if available) with answer for each questions. :)TOPIC: STATSTIC QUESTIONS: 7I AM HURRY FOR THIS REVISION :0 THANK YOU :)AMA1006 Basic Statistics, AMA1104 Introductory Probability

Assignment 1

Due

1

at 17:00, February 22, 2016, Monday. Please submit your homework into the assignment

box at foor 7 or 8, core T. The assignment box will be available ±or about one week ahead o± the

deadline, and with the

lecturer’s name

printed on the ±ront.

The markers o± the assignments are research students ±rom department AMA. Please show your

courtesy to them by

boxing

your ²nal solutions, like:

...therefore the desired probability is

P

(

A

)=0

.

334

.

Full marks: 100.

1. (10 marks) To test the quality o± a shipment o± crystal glasses, we selected 62 glasses at random.

We ±ound that two were scratched and chipped, three had only scratches, and ²ve were only

chipped. We randomly select two glasses,

X

and

Y

, out o± these 62 ones. Consider the

±ollowing events:

A

:

{

X

is chipped

}

, and

B

:

{

Y

is scratched

}

. Determine the relative

±requencies o±

A

,

B

,

A

?

B

, and

A

?

B

. Are the events

A

and

B

independent?

2. (20 marks)

a. I± two balanced dice are rolled, what is the probability that the sum o± the two numbers

that appear is odd?

b. I± two balanced dice are rolled, what is the probability that the sum o± the two numbers

that appear is even?

c. I± two balanced dice are rolled, what is the probability that the di±±erence between the

two numbers that appear will be no less than 5?

d. I± three ±air coins are tossed, what is the probability that all three ±aces will be the same?

3. (20 marks) How many di±±erent ways can one make a 5-digit number using digits

1

,

2

,

···

,

9

(but not 0), such that

a. each digit appears at most once?

b. each digit appears at most twice?

c. each digit may appear any times?

d. each digit appears at most once and digits in the number appear in an ascending order

(like 13456 but not 14365)?

Hint: Think each digit as a card. In (a) you have 9 such cards but in (b) you have 18. Use

multiplicative rule ±or (c) and combinations rule ±or (d).

4. (10 marks) A box contains 24 light bulbs, o± which two are de±ective. I± Tom selects 10 bulbs at

random, without replacement, what is the probability that both de±ective bulbs will be selected?

What is the probability that only one de±ective bulbs will be selected?

1

FAQ: “What i± I am sick on the day o± deadline?” ANS: you are encouraged to submit the assignment days be±ore the

deadline; in the worst case scenario you may take photos o± your whole assignment and email it to the lecturer be±ore the

deadline and we will print it out, and submit it to the marker ±or you; otherwise you would need a medical certi²cate ±or

us to accept your late submission.

1

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This question was answered on: * Sep 21, 2023 *

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