Transcript
Note:
Include ALL steps;
Use four significant digits;
Use a calculator;
Due at the beginning of next class meeting.
Read the statement with Extreme Care!
Name: Tian Yu Email: tian.yu@snhu.edu
Section 9.1 Probability Distribution and Expected Value
Question 21. (20 Points)
Business An online gambling site offers a first prize of $50,000 and two second prizes of $10,000 each for registered users when they place a bet. A random bet will be selected over a 24-hour period. Two million bets are received in the contest. Find the expected winnings if you can place one registered bet of $1 in the given period.
Ans:
x
$49,999
$9,999
-$1
P(x)
1/2,000,000
2/2,000,000
1,999,997/2,000,000
The expected winnings
49,999×12,000,000+9,999×22,000,000+-1×1,999,9972,000,000=-1,930,0002,000,000=-0.965
Section 9.2 Multiplication, Permutations, and Combinations
Question 58. (20 Points)
Finance A financial advisor offers 8 mutual funds in the high-risk category, 7 in the moderate-risk category, and 10 in the low-risk category. An investor decides to invest in 3 high-risk funds, 4 moderate-risk funs and 3 low-risk funds. How many ways can the investor do this? (Hints: determine whether the ordering matters.)
Ans: 8C3×7C4×10C3=8!5!3!×7!3!4!×10!7!3!=56×35×120=235,200
Section 9.3 Application of Counting
Two cards are drawn at random from an ordinary deck of 52 cards (no jokers). Find the probability that the 2-card hand contains the given cards.
Question 15. (10 Points) No deuces (2’s).
52C1×51C1=52!51!1!×51!50!1!=52×51=2,652
Question 19. (10 points) No more than 1 diamond.
There are 13 diamond cards in the total 52 cards.
No diamond: 39C1×38C1
1 diamond: 39C1×13C1
39C1×38C1+39C1×13C1=39!38!1!×38!37!1!+39!38!1!×13!12!1!=39×38+39×13=1,482+52=1534
Section 9.4 Binomial Probability
Social Science. According to the Website Anwers.com, 10-13% of Americans are left-handed. Assume that the percentage is 11%. If we select 9 people at random, find the probability that the number who are left handed is
Question 32. (20 Points)
at least 2;
At least 2 means 2,3,4,5,6,7,8,9
Px=0=9C0p0(1-p)9-0=9C0×0.110×0.899=9!9!0!×0.110×0.899?0.0385
Px=1=9C1p1(1-p)9-1=9C1×0.111×0.898=9!8!1!×0.111×0.898?0.3897
Pat least 2=1-0.0385-0.3897=0.5718
Question 34. (20 Points)
At most 3.
At most 3 means 0,1,2
Px=0=9C0p01-p9-0=9C0×0.110×0.899=9!9!0!×0.110×0.899?0.0385
Px=1=9C1p1(1-p)9-1=9C1×0.111×0.898=9!8!1!×0.111×0.898?0.3897
Px=2=9C2p2(1-p)9-2=9C2×0.112×0.897=9!7!2!×0.112×0.897?0.1927
Pat most 3=0.0385+0.3897+0.1927=0.6209
Bonus:
Question 35. (10 Points) In a class of 35 students, how many left-handed students should the instructor expect?
35×11%=3.85?4
