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13 days ago

8

A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly,

what is the probability that it is a valid number

1 answer:

PIT_PIT [3.9K]13 days ago

8 0

Answer:

$P(valid) = 1 * 10^{-8}$

Step-by-step explanation:

First, we need to calculate how many potential credit card numbers can be created using the digits 0 through 9.

We aim to create a number that consists of 16 digits from a total of 10 digits, therefore:

$N = 10^{16}$

The total count of possible numbers formed is $10^{16}$ . However, only 100 million of these are valid ( $100 * 10^6 = 10^8$ ). Let n represent the valid number of combinations.

This leads us to the probability of selecting a valid number:

P(valid) = n / N

$P(valid) = 10^{8} / 10^{16}\\\\P(valid) = 1 * 10^{-8}$

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Answer:

The shaped region accounts for 7/18 of the area of ACIG.

Step-by-step explanation:

Refer to the attached diagram for further clarity on the problem.

Step 1

Determine the length of one side of square ABED.

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The area of a square can be calculated as

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$b=7\ units$

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Step 2

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Step 3

Determine the area of the shaded rectangle DEHG.

The area of rectangle DEHG is given by

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Step 4

Calculate the area of shaded rectangle BCFE.

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Step 6

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