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Sagot :
Using the arrangements and the probability concept, it is found that there is a 0.75 = 75% probability that the number formed is not divisible by 4.
- A probability is the number of desired outcomes divided by the number of total outcomes.
- The number of possible arrangements of n elements is given by [tex]A_n = n![/tex]
In this problem, there are 4 elements, hence [tex]n = 4, T = A_4 = 4! = 24[/tex].
A number is a multiple of 4 if the number composed by it's last 2 digits are multiples of 4.
- Hence, the possible options for the last 2 digits are: 56, 68, 76.
- For each of them, there are [tex]A_2 = 2! = 2[/tex] options for the first 2 digits, hence, there will be 2 x 3 = 6 multiples of 4.
The other 18 numbers formed are not divisible by 4, hence:
[tex]p = \frac{18}{24} = 0.75[/tex]
0.75 = 75% probability that the number formed is not divisible by 4.
For more on arrangements and probabilities, you can check https://brainly.com/question/24437717
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