A box contains 40 number tiles numbered 1 to 40. If a tile is drawn at random, what is the probability that the number drawn is a multiple of 3 or 4? Find P(Multiple of 4 or Multiple of 5)

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A box contains 40 number tiles numbered 1 to 40. If a tile is drawn at random, what is the probability that the number drawn is a multiple of 3 or 4? Find P(Multiple of 4 or Multiple of 5)

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FelisFelis

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Explanation 1 P (3 or 4):
There are 40 number tiles numbered 1 to 40.
Multiple of 3 in 1 to 40 are:
There are 10 multiples till 30 (since $3 \times 10 = 30$ ) and then 33, 36, and 39 are other three multiples till 40. So there are 13 multiples of 3 from 1 to 40.
Multiples of 4 in 1 to 40 are:
There are 10 multiples till 40 (since $4 \times 10 = 40$ ) . So there are 10 multiples of 4 from 1 to 40.
Common Multiples of 3 and 4 in 1 to 40 is,
12, 28, 36, only 3
So, the probability of 3 or 4 is,
$P(\text {mult of 3})+P(\text {mult of 4}) -P(\text {mult of 3 and 4})$
$=\frac{13}{40} +\frac{10}{40} -\frac{3}{40}$
$=\frac{23}{40} -\frac{3}{40}$
$=\frac{20}{40}$
$=\frac{1}{2}$
So the probability of 3 or 4 is $\frac{1}{2}$ .

Explanation 2 P(4 or 5):
Multiples of 4 in 1 to 40 are:
There are 10 multiples till 40 (since $4 \times 10 = 40$ ) . So there are 10 multiples of 4 from 1 to 40.
Multiple of 5 in 1 to 40 are:
There are 8 multiples in 40 (since $5 \times 8 = 40$ ). So there are 8 multiples of 5 from 1 to 40.
Common Multiples of 4 and 5 in 1 to 40 is,
20 and 40 only 2
So, the probability of 4 or 5 is,
$P(\text {mult of 4})+P(\text {mult of 5}) -P(\text {mult of 4 and 5})$
$=\frac{10}{40} +\frac{8}{40} -\frac{2}{40}$
$=\frac{18}{40} -\frac{2}{40}$
$=\frac{16}{40}$
$=\frac{2}{5}$
So the probability of 4 or 5 is $\frac{2}{5}$ .
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