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Answer:
[tex]\dfrac{2} {5}[/tex]
Step-by-step explanation:
Probability represents the likelihood of an event occurring divided by the total possible events. Make sure to look at the keyword or in the multiple of 4 or 5. This means the ball just needs to be a multiple of only 1 of these numbers and if both occur, make sure to not double count them as a possible event.
Solving:
[tex]\subsection*{Number of Events:}\[\text{Total number of balls} = 40\]\hrulefill\\\\The multiples of 4 between 1 and 40 are: \[ \boxed{4, 8, 12, 16, 20, 24, 28, 32, 36, 40 }\]\[\text{Number of multiples of 4} = \left\lfloor \frac{40}{4} \right\rfloor = 10\]\\[/tex]
[tex]\subsection*}The multiples of 5 between 1 and 40 are: \[ \boxed{5, 10, 15, 20, 25, 30, 35, 40} \]\[\text{Number of multiples of 5} = \left\lfloor \frac{40}{5} \right\rfloor = 8\][/tex]
[tex]\hrulefill[/tex]
[tex]\subsection*{Multiples of Both 4 and 5 (Removing the doubles)}The multiples of 20 between 1 and 40 are:\[ \boxed{20, 40 }\]\[\text{Number of multiples of 20} = \left\lfloor \frac{40}{20} \right\rfloor = 2\][/tex]
[tex]\[\text{Number of multiples of 4 or 5} = \\(\text{Number multiples 4}) + (\text{Number multiples 5}) - (\text{Number multiples of both 4 and 5})\]\[= 10 + 8 - 2 = \boxed{16}\][/tex]
[tex]\hrulefill\\\\\[\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{16}{40}\]\\\[\frac{16}{40} = \frac{4}{10} =\boxed{ \frac{2}{5}}\][/tex]
Therefore, the probability that the randomly drawn ball is a multiple of 4 or 5 is 2/5.