The Math Of Broken iPhones

There're 20 parts that have $99.9\% = \frac{999}{1000}$ chance of not failing.

We'll find by using

P(Failing) = P(Total chance) - P(Not failing) = 1 - P(Not failing)

The chance that it will not fail = $(\frac{999}{1000})^{20}$ .

Therefore, P(Failing) = 1 - $(\frac{999}{1000})^{20}$ = 0.0198111351705. $\boxed{ 2 }$ ... *Fail, can't type %

We write all possibilities as a binomial expansion: $(S + F)^{20} = 1$ , where S is the chance for success and F is the chance for failure. Expanding, we have $S^{20} + ... = 1$ . All of the omitted terms contain at least one failure, so this is equivalent to writing $S^{20} + P = 1$ , where P is the chance of a failure. Thus $P = 1 - S^{20} = 1 - .999^{20} = .0198$ , which we round to 2%.

One might have an inclination to multiply 0.1% $\times$ 0.1% $\times$ 0.1% ... 20 times. However, this would actually be the probability of all 20 components failing in one year.

Instead, we need to find the complement of the case of none of the components breaking.

To begin, we acknowledge that there is a 99.9% chance that a single component does not break during the first year. (100% - 0.1% = 99.9%)

Next, to find out the probability of none of the components breaking in the first year, we find 99.9% $^{20}$ : 0.999 $^{20}$ = 0.980...

Finally, to find out the chance of at least one component breaking we subtract this from 100%: 100% - 98% = 2%

The chance for the components of iPhones to function properly in its first year is 0.999 (1.0-0.001=0.999).

Since the 20 components are independent, we multiply 0.999 by 0.999 20 times, i.e. (0.999)^20 to compute for the chance of the overall system (since it is a series circuit).

(0.999^20 = 0.9801888648)

Thus, the chance for the iPhone to function properly is approximately 98%. Accordingly, the chance for the iPhone to fail is 2%.

Hence, the answer is 2. :)

0.1% times 20 (there are 20 crucial parts) = 2%

there are 20 components. So, 20 *0.1= 2%.

0.1*20=2

(0.1%)x 20 = 2% so in that case the answer will be 2%

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Each component have the probability of failing in one year is 0.1%. There are such 20 components. So just simply add all their probabilities. The ans is 2

Chance of failing of one component = 0.1% = 1/100 (converted percent to fraction).Now, there are 20 components. let's assume that all component failed and chances of failing of all 20 components is 20 * (1/100) = 1/50 or 0.02. multiplying by hundred we get 2% that's the answer.

20 components x 0.1 = 2 percent

if any one component fails i phone will be failed if 2 components failed i phone will be failed .... so on then probability to fail is p= 20c1 0.1/100 + 20c2 0.1/100+......so on % chance to be failed is p*100=2.019 nearly 2

0.1/100 = 0.001 0.001 20= 0.02 0.02 100=2

20x0.1=2%

20*0.1=2

since each component has a independent failure chance of 0.1% ,i phone has 20 crucial components , 20*0.1=2,i.e 2% is chance of iPhone will malfunction in the first year.

0.1% x 20 = 2%

It is very simple..... I phone malfunctions when any one part does not work. so selecting at least one piece out of 20 is 20C1. now the chances of the part getting damaged is 1/10 times.... thus the chance for the phone getting damaged is 20C1 (1/10). it is equal to 20 .1=2 **Here C represents Combination

20 crucial components, 0.1% of chance to malfunction for each component. Then divide 20 by 0.1. It gives you 2.0. That is 2%.

a.t.q as there is a chance 0.1% of malfunctioning within the 1st year. i.e. 01 out 100. since , there is 20 crucial components. i.e. 20 crucial components in 100 components . so the final ans is given in such a way : 20 * 0.1 * 1/100 * 100=2

.1*20=2

its very easy if 20 parts are there each ha failing capacity of 0.1% so 2*0.1=2

Let $F$ denote the event that a component in the iPhone fails and $N$ denote the event that it does not fail.

$P(F) = 0.001$ and thus $P(N) = 1 - P(F) = 0.999$

We have to find out the probability that the iPhone fails. The iPhone will fail even if one component fails.

The probability that at least one component fails (thereby making the iPhone fail) can be calculated as $1 - P(\text{no component fails})$

Now, we find the probability that no component fails. That is simply $0.999^{20}$

Thus, the probability of the iPhone failing is $1 - 0.999^{20} \approx 0.0198$ giving us $\approx 1.98\%$ or rounded up, $\boxed{2}$

THERE ARE TOTALLY 20 PARTS EACH HAS A PROBABILITY OF FAILING 0.1 FOR 20 THE FAILING PROBABILITY IS 20*0.1=2%

This can be easily solved using the complement method. The chance that the iPhone will malfunction in the first year is the complement of the chance that it doesn't. So... $P(\mbox{working}) = 1 - P(\mbox{not working})$

This is the chance that every one of the parts doesn't malfunction that year, and every part has a 99.9% of not failing. So

$P(\mbox{not working}) = 0.999^{20} \approx 0.9801$ , therefore

$P(\mbox{working}) = 1 - 0.9801 \approx 0.02$

simple solution........since 20 parts,....therefore....20x0.1%= 2 which is the required answer...

the probability of not getting malfunction for each component is 1-0.001=.999 the probability of that all the component will work well= .999 to the power 20 =0.9801 the probability that i phone will create malfunction = 1-0.9801=0.0198

just simple: 20 (crucial components) x (multiply) with 0.1% = 2%

20 x 0.1% = 2%

Why the hell any one would do this on calculator ?

Simple as that, parts=20 percentage=0.1 per annum =20/0.1/100

save time. go by common sense. 1 part has chance of failing is 0.1 %. therefore 20 parts together has a chance of failing = 20 *0.1 =2% of failing. simple

.1%= .001. Therefore .001*(20 components)=.02 or 2%.

There is a 0.1% chance for each part to malfunction, and there are 20 parts, so when you do 20 times 0.1 you get 2%. The correct answer is 2.

0.1% x 20 = 2%

By complementary counting, the answer is 1 minus the probability that the iPhone does NOT fail.

The probability that a component doesn't fail is 1 minus the probability that it does fail, which would be 0.999.

The probability that the iPhone fails is that to the twentieth power.

Now, take 1 minus that, and rounds to 2.

0.1 x 20 = 2.0