(Solution) 12/13 Spring THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2601 Probability & Statistics I Assignment 1 Due | Snapessays.com


(Solution) 12/13 Spring THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT2601 Probability & Statistics I Assignment 1 Due


I have problems in question 3,7,13,16,20,29,42,4512/13 Spring

 

THE UNIVERSITY OF HONG KONG

 

DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE

 

STAT2601 Probability & Statistics I Assignment 1 Due Date: February 21, 2013 (Hand in your solutions for Questions 3, 7, 13, 16, 20, 29, 42, 45, 47) 1. A total of 7 different gifts are to be distributed among 13 children. How many distinct results are possible if no child is to receive more than one gift? 2. From a group of 8 women and 6 men a committee consisting of 4 men and 4 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together;

 

(b) 2 of the women refuse to serve together;

 

(c) 1 man and 1 woman refuse to serve together?

 

3.

 

In how many ways can 12 people be seated in a row if

 

(a) there are no restrictions on the seating arrangement;

 

(b) persons A and B must sit next to each other;

 

(c) there are 6 men and 6 women and no 2 men or 2 women can sit next to each other;

 

(d) there are 5 men and they must sit next to each other;

 

(e) there are 6 married couples and each couple must sit together?

 

4. Four separate awards (best scholarship, best leadership qualities, and so on) are to be

 

presented to selected students from a class of 25. How many different outcomes are possible

 

if

 

(a) a student can receive any number of awards;

 

(b) each student can receive at most 1 award?

 

5. (

 

Poker

 

)

 

If it is assumed that all

 

poker hands are equally likely, what is the probability of being

 

dealt

 

?

 

?

 

?

 

?

 

?

 

?

 

?

 

?

 

5

 

52

 

(a) one pair? (This occurs when the cards have denominations

 

a, a, b, c, d

 

where

 

a, b, c,

 

and

 

d

 

are all distinct.)

 

(b) two pairs? (This occurs when the cards have denominations

 

a, a, b, b, c

 

, where

 

a, b,

 

and

 

c

 

are all distinct.)

 

(c) three of a kind? (This occurs when the cards have denominations

 

a, a, a, b, c

 

.)

 

(d) a straight? (Five consecutive cards of any suits which are not all the same, including

 

10, J,

 

Q, K, A

 

.)

 

(e) a flush? (Five cards of the same suit and not all in consecutive order.)

 

(f) full house? (This occurs when the cards have denominations

 

a, a, a, b, b

 

.)

 

(g) four of a kind? (This occurs when the cards have denominations

 

a, a, a, a, b

 

.)

 

(h)

 

a straight-flush? (Five consecutive cards of the same suit, including

 

10, J, Q, K, A

 

.)

 

6.

 

From a group of 4 lawyers, 8 accountants, and 7 doctors, a committee of three is selected at

 

random. What is the probability that the committee has more lawyers than doctors?

 

P. 1

 


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