×

# Probabilities Of A Happy Chinese New Year

(12)
Tuition given in the topic of E-Maths Tuition Questions from the desk of at 12:03 pm (Singapore time)

Updated on

Feeling particularly auspicious on a Chinese New Year day, and trying to escape the subliminal effects of the endlessly-repetitive new year songs being played at the malls, Miss Loi joins a game of mahjong with the Trusty Webmaster, her friend Miss Thong, and … umm … a complete newbie who’s there simply because of 三缺一.

That missing tile. HUAT AH!
(source)

In one particularly tense game, with only 16 tiles left to be drawn, three of them happened to be “waiting” for the same tile: a green 發财 – Miss Loi to complete her 十三么 (The Thirteen Wonders), Miss Thong to complete her 大三元（The Three Scholars), Trusty to complete his pair for his 大四喜 (Four Great Blessings). As for the Newbie, well … let’s just say that everyone would be happy if she doesn’t 詐胡 in the first place.

Given that:

• The final 發财 lies amongst the last 16 tiles.
• It’s now Miss Thong’s turn, followed by Trusty Webmaster, Newbie, and Miss Loi, in that order.
• Being THE Newbie with absolutely zero sense of strategy, she has a probability of 0.5 of throwing out any tile that she draws.

Calculate the probability that Miss Loi will win this game and sweep the table with her 十三么 by the time it comes to her turn!

Please note that Miss Loi does NOT advocate nor encourage any form of gambling but nevertheless she hopes that this will make all you be more aware of the odds you might be facing in the next few days of the festive season 😀

WARNING: As not everyone is familiar with the rules of the game, there is absolutely ZERO chance that an exact question like this will appear in your test or exam, though it may assume other forms, like drawing some coloured balls from a sack *yawwn*

### Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

Comments & Reactions

### 12 Comments

1. FoxTwo commented in tuition class

2008
Feb
6
Wed
12:19pm

1

Alas... the only Mahjong I play is the "match the same tiles" type, on the arcade machines 🙂

2. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Feb
6
Wed
3:50pm
3. imp commented in tuition class

2008
Feb
6
Wed
5:53pm

3

Arrgh! Screw probabilities! I flunked that royally years ago. I say, you WILL have a great year ahead Miss Loi, abound with calm, health and peace and determination in the temple!

4. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Feb
6
Wed
6:47pm

4

imp, and you'll have a faerie year abound with great travels, great food, and love all around you 🙂

P.S. Errr ... probabilities are probably one of the most practical and down-to-earth topics in maths. Take this case ... you see ... if you're a true-blue mahjong tai-tai there are really only two ways in which Miss Loi can win when it reaches her turn 😉

5. FoxTwo commented in tuition class

2008
Feb
6
Wed
10:01pm

5

Err... no SMC, I'm Chinese. I just never bothered to learn how to play Mahjong the proper way 🙂

Besides, the only thrill of playing Mahjong is to win money, and since I'm a non-gambler, no incentives to learn it.

6. game commented in tuition class

2008
Feb
7
Thu
11:49pm

6

In my City everyone like playing Mahjong I am from chinese

7. ByPassing commented in tuition class

2008
Feb
8
Fri
12:39am

7

Yah~Wishing you ratmarkable probability on the mahjong table.

8. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Feb
8
Fri
1:23pm

8

FoxTwo: Relax ... just pulling your leg 😀

game: 恭喜恭喜！您现在在大陆哪里过年啊？

ByPasser: Oh thanks! Wishing you many many Thirteen Wonders!

9. FoxTwo commented in tuition class

2008
Feb
9
Sat
1:15pm

9

You changed the question!!!!

From a 中 tile you changed it to a 發 tile!

CHEAT!!! :p

10. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Feb
9
Sat
7:00pm

10

Shhh ... not so loud!

Miss Loi's already feeling utterly ashamed that her wily 老千 maneuver was caught by a mahjong newbie!

But then again, the question essentially remains unchanged, and don't you agree that a 發财 sounds more prosperous than a 紅中? 😛

11. Anoneemers commented in tuition class

2008
Oct
25
Sat
5:36pm

11

Sianz mahjong so hard to understand...nid mahjong+maths experts to solve and
P(a person is good in both mahjong and maths)=1/100
Is the answer 15/16 X 14/15 X 13/14 X 1/13 = 1/16 (assuming all other players didnt discard their tiles)
or 15/16 X 15/16 X 15/16 X 1/16 = 3375 /65536 ? (assuming all discard if not the 發财 tile)

P.S.If this question ever comes out in exam i will probably write P(win)=1/2 (win or lose XD).

12. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Oct
29
Wed
1:11am

12

LOL first of time Miss Loi would like to state that such a question will confirm chop stamp NEVER EVER appear in your exam ... Heee ...

So we have:

• P(Miss Thong doesn't draw the 發) = 15/16
• P(Trusty doesn't draw the 發) = 14/15 (coz less one tile by the time it comes to Trusty's turn)
• P(Newbie doesn't draw the 發) = 13/14 (coz less one tile by the time it comes to Newbie's turn)
• P(Newbie draws the 發 AND she throws it out) = (1/14)(1/2)
• P(Miss Loi draws the 發) = 1/13 (i.e. 自摸! - can only reach this stage if Newbie doesn't throw the 發 out for Miss Loi to win)

To obtain the probability of Miss Loi winning, you'll need to add up all the possible cases that she will win i.e.

1. 自摸 Case! i.e. P(Miss Thong doesn't draw the 發) x P(Trusty doesn't draw the 發) x P(Newbie doesn't draw the 發) x P(Miss Loi draws the 發)
2. Thank You Newbie Case! i.e. P(Miss Thong doesn't draw the 發) x P(Trusty doesn't draw the 發) x P(Newbie draws the 發 AND foolishly throws it out for Miss Loi to win!)

∴ P(Miss Loi wins!) =
(15/16)(14/15)(13/14)(1/13) + (15/16)(14/15)(1/14 x 1/2)
= 1/16 + 1/32 = 3/32

So Anoneemers would you like to join us at the mahjong table? 😉

• ### Latest News

A New Year. A New Hope.

Hybrid joss sticks math tuition sessions are continuing to be conducted both online and onsite at Novena in 2024.

Please check our latest 2024 Jφss Sticks weekly secondary / O level maths group tuition schedule for updates.

Subscribe now to Miss Loi's Maths Exam Papers are now available for immediate online purchase.

... and join our ever-growing list of subscribers

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

• ### About Miss Loi

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life’s calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over years she has been a savior to countless students … [read more]

### Gratitudes

For the 3 months that I have attended her class, I have done more than I thought I was capable of – LIKE PASSING MY PRELIMS … [read more]

Stephanie Tan
St. Nicholas Girls’ School