Kyle has a lock combination with three digits. Every number in the combination must be a 0-4. What is the probability that his combination is 000?

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gsenviro | College Teacher | (Level 1) Educator Emeritus

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Probability of getting 0 as a digit, p = 1/5 (only one chance in 5, other options could be 1,2,3,4)

Probability of not getting 0 as a digit, q = 1-1/5 = 4/5

The probability of getting 000 as lock combination is same as getting the 0 three times in a row. We can use the following equation to solve the question:

`P(x=k) = (n k) p^k q^(n-k)`

Here, k =3,

Therefore the probability, P = (3  3) `(1/5)^3 (4/5)^(3-3) = (1/5)^3 = 1/125`

Hope this helps.

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Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

gsenviro's method of solving this problem is just as valid as mine. My method, however, is easier for simpler questions such as these. If you do not understand his method at all, I still advise you to try to learn it. For sure, there WILL be more advanced probability questions that would, for instance, instead of asking for the probability of just 000, would rather ask for the probability of the combinations that simply just have the number 0 in them. From there, gsenviro's method would be much easier to use to achieve the answer.

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Nolan McShea | Student, Grade 11 | (Level 2) Honors

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Kyle has a lock combination of three digits. Each of those numbers can be either 0, 1, 2, 3, or 4. Those are five numbers.

To get the total amount of combinations, you can basically do this:

`5^3`

Five cubed, or five to the third power. The five means that there are five numbers, and the three means that there is three slots for those five numbers. So, basically,

`5^3=5*5*5`

5 cubed means five multiplied by itself three times. So, if we do that,

`5*5=25;`

`25*5=125`

Thus, 125 is the total amount of combination possibilities for Kyle's lock.

Now, what is the probability of Kyle's lock being 000? Well, 000 is only one combination. So, that's one combination out of the 125 TOTAL possibilities for his combination. Given that, we can create the fraction

`1/125`

I hope I helped!

In case you need to know the percentage, you can just do 1/125 and get a decimal 0.008, which means there is a 0.8% chance of his locker combination being 000.

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