TS12:55:00 AM

TS5:22:00 PM

After class activity, DOTA!

:D

Who wants a CHALET ?
http://www.aloharesorts.com.sg/

Who wants a CHALET ?
Who wants a CHALET ?
Who wants a CHALET ?

Loves, Min Er

TS3:43:00 PM

TS3:27:00 PM

TS3:33:00 PM

Problem 08 Math WS ans
1. Yes, there is a probability that I might win if I switch my initial box.
No , because I have chosen 1 out of 3 if i choose again it will be 1/3*1/2
2. 1/3*1/2 or ½
3.
4.
Game
Player 1
Player 2
1
WIN
LOSE
2
LOSE
WIN
3
WIN
LOSE
4
WIN
WIN
5
WIN
LOSE
6
LOSE
WIN
7
WIN
LOSE
8
LOSE
LOSE
9
LOSE
LOSE
10
WIN
LOSE
11
WIN
LOSE
12
WIN
LOSE
13
WIN
LOSE
14
WIN
WIN
15
WIN
LOSE
16
WIN
WIN
17
LOSE
LOSE
18
LOSE
LOSE
19
WIN
LOSE
20
WIN
WIN
21
WIN
LOSE
22
LOSE
LOSE
23
LOSE
LOSE
24
WIN
LOSE
25
WIN
LOSE
26
WIN
LOSE
27
WIN
LOSE
28
LOSE
LOSE
29
WIN
LOSE
30
WIN
LOSE
5. Change – 21/30
Same – 6/30
I would choose the one that changed because there is a higher chance of winning.
Initial Choice made by contestant
Outcome
Box 1
Lose
Box 2
Win
Box 3
Win
Initial Choice made by contestant
Outcome
Box 1
Win
Box 2
Lose
Box 3
Lose
6.





7. The probability of winning is higher in strategy 1 than strategy 2.
If we switch our chance will be separated to 50% but if we do not switch our first choice must win if not we will go straight to lose
It is better to switch that no to switch always as there is a higher chance of winning.
8. No, it does not affect the conclusion we made in question 7.
9. Always switch strategy
10. Finding out the probability of winning the game and make our decisions according to the option with the higher probability so as to have a higher chance of winning.
11.
Game
Outcome
1
Correct
2
Wrong
3
Wrong
4
Wrong
5
Correct
6
Wrong
7
Correct
8
Correct
9
Correct
10
wrong
11
Correct
12
Correct
13
Wrong
14
Correct
15
Wrong
16
Wrong
17
Wrong
18
Correct
19
Wrong
20
Correct
21
Correct
22
Correct
23
Correct
24
correct
25
Correct
26
Wrong
27
Wrong
28
Wrong
29
Wrong
30
Correct
12. It leads to more correct guesses.
13. 13a. 2/3 of the chance to win 1/3 to lose
b. 2/6
c. X or O
d. No, I would not change as there is still a higher chance of choosing the correct cards when choosing the cards with the same signs
14.
15.
Scenarios
Possible Worlds
Probability
a. heads in all three throws?
HHH
1/8
b. a head on the first throw?
HHT/HHH/HTT/HTH
1/2
c. a tail on the second throw?
TTH/TTT/HTH/HTT
1/4
d. two heads and one tail out of the three throws?
HHT/THH
2/8
e. at least one head out of the three throws?
HHH/HHT/HTH/HTT/THH/THT/TTH
7/8

16. Scenario E. 7/8. Because it has the highest probability.
17.
Scenarios
Possible Worlds
Probability
a. heads in all three throws?
HHH
1/8
b. a head on the first throw?
HTH/HHH/HHT/HTT
4/8
c. a tail on the second throw?
HTH/HTT
2/8
d. two heads and one tail out of the three throws?
HHT/HTH
2/8
e. at least one head out of the three throws?
HTT
1/8

18. In this case we have define that 1st throw has to be head , hence it has narrowed down our possible worlds that our 1st throw has to be H and cancel out the possible world of having the 1st throw T.
19. 0.6%(infected)
0.6% * 4,000,000 = 24,000(infected)
20.
Population
(4,000,000)
Infected with Hepatitis-C
( 20 000 )
Not Infected with
Hepatitis-C
( 3980000 )

Tested positive
( 19800 )
Tested
negative
( 200 )


Tested
positive
( 3940200 ) )

Tested
negative
( 30800 )



21. Infected, Tested +ve
Infected, Tested –ve
Not Infected, Tested +ve
Not Infected, Tested –ve
Or
4, separately HH,HT,TH,TT

22. Infected, Tested +ve
Not Infected, Tested +ve
H

23. Yes
Yes. The professor says that “the test kit is 99% accurate in giving the correct test result” does not mean that “there is a 99% chance that a person has the Hepatitis-C virus when the test kit shows a positive result” so, one single test will not accurately shows that Joshua really has Hepatitis-C.
or 1/4
No, as professor’s statement says that the answer should be 1/99
24.
25. There is a higher possibility of choosing the correct cards when we choose those cards with the same signs.

26. Yes, I should continue with my original strategy as still, there is a higher chance of me winning by choosing the cards with the same signs.

TS12:59:00 PM

TS11:25:00 PM