Quick Probability Question

[Pointlessness]

There are two bags, both containing 60 marbles that are either black or white. The first bag contains 30 white and 30 black marbles. You are told that in the second bag, you are twice as likely to draw a black marble compared to the first bag. How many black marbles are in the second bag?

 

[Quackers]

40:20

 

[civver_764]

I'm not seeing why it wouldn't be 60 and 0.

In the first bag there's a 50% chance of drawing black. 50*2 = 100. 100% of 60 is 60. What am I missing here?

 

[MrCynical]

Well with a 50% chance in the first one, doubling your chances would require 100% from the second, so 60/0.

This feels like one of those problems which is trying to use ambiguities in wording to allow multiple "right" answers to a mathematical problem. The other offered answers being 40/20 (twice the probability of drawing a black than a white for that bag only), and 45/15 (presumably from a 0.5*0.5 = 0.25 line of thinking). The question is really one of semantics, not maths.

 

[Leoreth]

I agree, "twice as likely" is a phrase I would avoid when talking about probabilities. But in my intuitive interpretation, it should be 60:0.

 

[Truronian]

60 black and 0 white is the only correct answer.

 

[Borachio]

Who says we have to find the correct answer?

But 60:0, I'd go with.

 

[Quackers]

60 black and 0 white is the only correct answer.

why am i wrong and why is that answer right mr teacher sir

 

[Leoreth]

See MrCynical's first sentence.

 

[warpus]

I agree, "twice as likely" is a phrase I would avoid when talking about probabilities. But in my intuitive interpretation, it should be 60:0.

I agree. The question seems to rely more on your interpretation and understanding of "twice as likely" rather than your understanding of probability and statistics.

 

[Truronian]

why am i wrong and why is that answer right mr teacher sir

P(Black in Bag 1) = 0.5

0.5 x 2 = 1

1 = P(certain event) ergo in bag 2 you're certain to get black.

 

[azzaman333]

There are two bags, both containing 60 marbles that are either black or white. The first bag contains 30 white and 30 black marbles. You are told that in the second bag, you are twice as likely to draw a black marble compared to the first bag. How many black marbles are in the second bag?

Key phrase bolded. So 60:0.

 

[Quackers]

ahh "compared to the first bag" makes so much more sense now. gotta read it more then once

 

[Zack]

P(black in bag 1) = 0.5

P(something sleazy involving your mother) = 1

ergo,

P(black in bag 2) = (1 + 0.5) / 2 = .75

.75(60) = 45

60 - 45 = 15

= 45 black marbles, 15 white marbles.

 

[Borachio]

But, in that case, how does 0.75 (the p of black in bag 2) = 2 x 0.5 (the p of black in bag 1)?

 

[Gigaz]

The problem is that "twice as likely" is rather ambiguos.

Alternatively to some of the interpretations above one can say that it describes the propability for at least one black marble when you draw two instead of one.

Both concepts converge to the same numbers for lower propabilities. If I buy two lottery tickets I have the double chance with either calculation to a very good degree of approximation.

 

[History_Buff]

P(Black in Bag 1) = 0.5

0.5 x 2 = 1

1 = P(certain event) ergo in bag 2 you're certain to get black.

This.

The problem is that "twice as likely" is rather ambiguos.

Not it isn't.

This really is a brilliant problem, because all you need to do to get it correctly is take the time to read and properly understand the question. Which is not overly difficult, and there is one clear meaning. These sorts of word problems are brilliant, and we need more of them.

 

[metatron]

The problem is that "twice as likely" is rather ambiguos.

Not really...

Alternatively to some of the interpretations above one can say that it describes the propability for at least one black marble when you draw two instead of one.

No.

1-(30/60)*(29/59) = 0.75 (-> original)
1-(20/60)*(19/59) = 0.89 (-> Quackers)
1-(15/60)*(14/59) = 0.94 (-> Zack)

I fail to see how anything in this is doubling. Unless you turn the whole thing around... you know... as a consequence of illiteracy or something like that.

 

[Leoreth]

The phrase "twice as likely" itself is ambiguous without the later qualifier "compared to the first bag".

 

[potatokiosk]

The probability of drawing the first bag out of the second bag is zero. So if the probability of drawing a black marble is twice as likely as compared to the first bag, there can't be any black marbles, because two times zero is zero.