We love math

[arzafar]

1. 11,500= 10,000 + 3*500

2. .0625= 1/ 16

I'm assuming that you pick the box after answering the questions. Otherwise... if you choose at the onset. 15 box would remain. And, they'd have to split one box into 2!

3. 50%

4. 16/2 =8 (1st question correctly answered)
8/2= 4 (2nd question correctly answered)
4/2= 2 (3rd question correctly answered)


...I hope there's such a TV game show. I would wan to be a contestant!

*Question: has anybody here taken the GMAT, or will take one? any tips would be appreciated just reminded me because I heard there is a part where you have to decide whether the problem statement is enough to draw a conclusion...

*Also, look down at the thread suggestions. It' all pertains to love. haha!

same as above except no 3.

3.) 1 - {(1/2)^3 [all 3 answers wrong] x (15/16) [choose the box without the $10K]} = 113/128

 

[rayray]

same as above except no 3.

3.) 1 - {(1/2)^3 [all 3 answers wrong] x (15/16) [choose the box without the $10K]} = 113/128

oh yeah you're right... Where's Ayman the cayman? He should give more!

 

[arzafar]

Yes. That's the only way to win the $10,000. The questions are meant to improve the contestant's chances.



Correct, except 3. Good work!

The reason that the probability of winning all the money is 1/16 is because you must answer all three questions correctly and the probability of that is 1/2x1/2x1/2 = 1/8. Then you have to guess between the two remaining boxes, so multiply by another 1/2 giving you 1/16.



Correct. It is interesting that it is quite higher than 50%, which makes the game biased toward winning. Nice from the producers of The Price Is Right, isn't it?

more calculation required
R - right answer,
W - wrong answer

to win $zero
probability = (WWW) x 15/16 = 1/8 x 15/16 = 15/128

to win $500
probability = (RWW + WRW + WWR) x 7/8 = 3/8 x 7/8 = 21/64 = 42/128

to win $1000
probability = (RRW + RWR + WRR) x 3/4 = 3/8 x 3/4 = 9/32 = 36/128

to win $1500
probability = (RRR) x 1/2 = 1/8 x 1/2 = 1/16 = 8/128

to win $10k
probability = (WWW) x 1/16 = 1/8 x 1/16 = 1/128

to win $10.5k
probability = (RWW + WRW + WWR) x 1/8 = 3/8 x 1/8 = 3/64 = 6/128

to win $11k
probability = (RRW + RWR + WRR) x 1/4 = 3/8 x 1/4 = 3/32 = 12/128

to win $11.5k
probability = RRR x 1/2 = 1/8 x 1/2 = 1/16 = 8/128

check probabilities (sum = 1)
(15+42+36+8+1+6+12+8)/128 = 1

so expected return per game =
[(0 x 15) + (500 x 42) + (1000 x 36) + (1500 x 8) + (10000 x 1) + (10500 x 6) + (11000 x 12) + (11500 x 8)]/128

= $2859.375

conclusion:
each game on average would costs the company $2859.375 so the game is biased in favor of the contestant.

However, the direct and indirect revenues generated from the game show would amount to millions of dollar per game

 

[hayat84]

:salam2:
what a patience you have...why does maths exist??I'm really sorry,but I can't resist by mocking you,cause maths has never been my favourite domain.Do have fun,bye bye

 

[hayat84]

:salam2:
try to pose me an easy problem and I try to solve it.I find maths interesting but I have no much patience.thanks