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a four digit number is formed from the digits 1, 2,3 and 5 without repetition. find the probability that a number chosen at random from these numbers is divisible by 4.

User Eldjon
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Final answer:

The probability that a randomly chosen four-digit number formed from the digits 1, 2, 3, and 5 without repetition is divisible by 4 is 0.1667 when rounded to four decimal places.

Step-by-step explanation:

To find the probability that a four-digit number formed from the digits 1, 2, 3, and 5 without repetition is divisible by 4, we need to know the divisibility rule for 4: a number is divisible by 4 if its last two digits form a number that is divisible by 4.


Since we are forming four-digit numbers, we need only consider combinations of the last two digits. There are six possible two-digit combinations from these digits: 12, 32, 52, 24, 14, and 34. Out of these, only 12 and 32 are divisible by 4.

These two combinations can be at the end of a four-digit number, and we can arrange the remaining two digits in the front in two different ways each (since they are not repeated).



Therefore, we have 2 (choices for the last two digits) × 2 (ways to arrange the first two digits) = 4 possible four-digit numbers that are divisible by 4. In total, there are 4! or 24 possible four-digit numbers that can be formed using the digits 1, 2, 3, and 5 without repetition.

Hence, the probability is calculated as follows:



Probability = Number of favorable outcomes / Total number of possible outcomes


Probability = 4 / 24


Probability = 0.1667 (rounded to four decimal places)

User Nirmal Ram
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