Math Is Fun Forum

BOBS
BIBS
BIGS
TIGS
TIGE →
TILE
TILP →
TULP

FOUR ⇒ ZERO ⇒ FIVE

Consider the following experiments..
1. Throwing two identical unbiased dies and getting a sum of 11.
CASE-I: you get a 5 on dies-1 and 6 on dies-2
CASE-II: the numbers swap.
Both the cases are different and acceptable.

2. Throwing a dies twice and getting a sum of 11.
CASE-I: you get a 5 on throw-1 and 6 on throw-2.
CASE-II: a 6 on throw-1 and 5 on throw-2.
The cases, again, are different and acceptable too!

Now consider the experiment dealing with babies exactly identical in > height, weight, date/time of birth, choices (if that matters) but with different possible sexes except of course for the case that both are girls}...
CASE-I: both are boys.
CASE-II: one (which one?) is a boy and the other is not.

This is in no manner similar to stating that the probability of drawing a card from a pack of 52 cards and its being an A is 1/2 (either it is an A or it is not) because if it ain't an A then there are 12 other possibilities.
On the other hand, in case of the problem in context, no other outcomes are possible.

Normally, it doesn't have ANY business (whatsoever) with Vegas.
Probability works only on papers. Probability that you'r an Asian is 40%!

Hi;

Throwing a die one at a time → Throw-1 and Throw-2
Throwing tow dies at once → Die-1 and Die-2

Think distinguishability of the events plays an important role here!
Both the experiments are Similar because the events can be Differentiated!

I Can't think of any suitable example resembling "Twins" right now.... Hope there must be.

Got it since the Sample Space is {(HH), (HT), (TH), (TT)} and there are Two favorable outcomes for "One of each"! (I wouldn't go about the crazy idea of trying flipping a coin myself though )

But this is fairly coz of one main reason... Coin-1 and Coin-2!!

Your next few words explain it More Clearly........

Nice explication of the effect of distinguishableness.

As i mentioned earlier.....

1/3 is possible for the case Child-1 (Younger) and Child-2 (Elder).

I'd set it that the probability is 1/2 if they are twins!?

I haven't yet thought about "a boy born on Tuesday" one...

But for the first one, the only possibilities are...
1. Both children are boys. (√)
2. Both children are girls. (x)
3. One of the children is boy and the other one is girls. (√)

I agree that the question is not framed properly since nothing is mentioned about who's younger/elder.
The question is analogous to possessing (order doesn't matter) two balls of different colors (say PINK and BLUE) and not to drawing two balls from two sacs of two different colored balls wherein the order of ball drawn matters!

Number of Readers Initially = 1000 = 1000×2[sup]0[/sup]

Number of New Readers..
at the end of 1[sup]st[/sup] year = (1000)×2 = 1000×2[sup]1[/sup]
at the end of 2[sup]nd[/sup] year = (1000×2)×2 = 1000×2[sup]2[/sup]
at the end of 3[sup]rd[/sup] year = (1000×2[sup]2[/sup])×2 = 1000×2[sup]3[/sup]
.
.
.
at the end of 10[sup]th[/sup] year = (1000×2[sup]9[/sup])×2 = 1000×2[sup]10[/sup]

Total Number of Readers at the End of 10 years...

⇒ 1000×2[sup]0[/sup]+1000×2[sup]1[/sup]+1000×2[sup]2[/sup]+1000×2[sup]3[/sup]+...+1000×2[sup]10[/sup]

⇒ 1000×(2[sup]0[/sup]+2[sup]1[/sup]+2[sup]2[/sup]+2[sup]3[/sup]+...+2[sup]10[/sup])

⇒ 1000×(2[sup]11[/sup]-1)

NOTE: This an example of Exponential Growth!

you mean as in (1100+12)[sup]2[/sup] = 1236544

xxxxxxxab and (a,b)≠(00, 44) 

Thanks Again! 

U2? Me too

Hope you'll enjoy this......

Where am i going wrong...

I didn't know this rule... I'll do one for you

LIFE ⇒ FIND ⇒ LOVE

LIFE
LINE
FINE
FIND
FINE
FIVE
LIVE
LOVE

PLAY ⇒ GAME ⇒ OVER