Mathematics, 21.03.2020 03:42 Sevara100

A thief steals an ATM card and must randomly guess the correct six-digit pin code from a 4-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?

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Answer from: Asterisk

The probability of a correct guess on the first try is 0.000244 or 0.0244%.

Step-by-step explanation:

Given:

Number of digits in the pin code = 6

Number of keys in each digit = 4

So, in order to get the correct pin code, the key selected in each digit should be correct.

So, there will be only 1 correct key in each digit.

Now, probability of selecting a correct key in first digit is given as:

$P(correct\ key)=\dfrac{Number\ of\ correct\ keys}{Total\ number\ of\ keys}\\\\P(correct\ key)=\frac{1}{4}=0.25$

Now, there are 6 digits in the pin code and repetition is allowed. So, the probability of selecting the correct key in the remaining digits will also be equal to 0.25.

Therefore, the combined probability of selecting the correct pin code in the first try is the product of probabilities of selecting each correct key in each of the digits.

So, $P(correct\ pin\ code)=(0.25)^6=0.000244$

Therefore, the probability of a correct guess on the first try is 0.000244 or 0.0244%.

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

how many players are there?

step-by-step explanation:

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A thief steals an ATM card and must randomly guess the correct six-digit pin code from a 4-key keypa...

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