# The Puzzling Phone [closed]

The amazing "Puzzling Phone", comes in two models, one sold by "Super Puzzling Inc", and one sold by "Mega Puzzling Ltd"

Phones need to have government testing before they can be sold on the market.

Through this testing, it turns out that a third of the "Super Puzzling Inc" models on the market work for over 10 hours on a single charge, and measurements have been conducted that revealed half of the "Mega Puzzling Inc" models last for over 10 hours on a single charge. Battery testing, as you all know, is very important! (:D)

"Super Puzzling Inc" is a very large company with a lot of resources, hence why 70% of the market is filled with its Puzzling Phones. The consumers have spoken and they simply like the new "Jet Black" colours that are available, which the other company doesn't sell. The new "Rose Gold" colours are also just wonderful!

You have completely randomly purchased a brand-new "Puzzling Phone", however, it is unlabeled, so you don't know which company of the two manufactured it, and additionally, you have not taken a look at the box or its contents at all.

What's the chance it lasts for more than 10 hours on a single charge? Assume that it was sold already fully charged from the beginning.

(Note: You should ignore any technological equipment such as the screen, processor, etc, and treat this as a mathematical question.)

• Comments are not for extended discussion; this conversation has been moved to chat.
– Deusovi
Jan 30, 2017 at 1:05
• That was the main confusion. Jan 30, 2017 at 1:25
• No. I'm not claiming that it is difficult. I'm saying that there is no answer. What actual information do you think we have?
– Deusovi
Jan 30, 2017 at 1:42
• I posted my answer before anyone claimed that there is no answer; how can it possibly have been a comment on that claim? Jan 30, 2017 at 10:36
• I've adjusted my answer so that it solves the basically-routine mathematics problem that the question has turned into. However, being a basically-routine mathematics problem this should surely be closed as such. Unless, of course, I'm missing something and it's not really a brmp. What I would actually like to know is what sort of answer CipherRiddle thought appropriate for the original version of the question. Jan 31, 2017 at 3:00

[The question has been edited and greatly changed in the process; so, accordingly, has my answer.]

(I don't see that this is actually a puzzle, unless there is some steganographic thing going on to give the actual answer.)

It's not perfectly clear what it means to say that you have "completely randomly" purchased a phone. I shall take it to mean something equivalent to this: Of all the phones of these two kinds to be sold this year, you picked a random one and bought it. This means that there's a 70% chance that your phone comes from SPI, and a 30% chance that it comes from MPL. In the first case, the probability of long battery life is 1/3; in the second, it's 1/2. Accordingly, the probability that your phone's battery is long-lived is 0.7*1/3 + 0.3*1/2 = 7/30+3/20 = 14/60+9/60 = 23/60.

If instead you had someone flip a coin and pick a brand corresponding to the result, your probability of long battery life is 1/2*1/3 + 1/2*1/2 = 5/12.

The original version of the question omitted all the specific numbers but still appeared to ask for an actual numeric answer. If the OP would care to explain how that was meant to work, I would be interested.

• I really appreciate this, but for questions like this I honestly think leaving them unanswered is better. (It's almost certainly going to be closed soon, anyway...)
– Deusovi
Jan 30, 2017 at 0:00
• I'm always in two minds about it. Jan 30, 2017 at 0:05
• (Note: the previous comments were written when the question took its earlier form -- though they may well apply equally to its current form.) Jan 31, 2017 at 2:58