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 [tex]3 \times 10 = 30[/tex]) 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 [tex]4 \times 10 = 40[/tex]) . 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,
[tex]P(\text {mult of 3})+P(\text {mult of 4}) -P(\text {mult of 3 and 4})[/tex]
[tex]=\frac{13}{40} +\frac{10}{40} -\frac{3}{40}[/tex]
[tex]=\frac{23}{40} -\frac{3}{40}[/tex]
[tex]=\frac{20}{40}[/tex]
[tex]=\frac{1}{2}[/tex]
So the probability of 3 or 4 is [tex]\frac{1}{2}[/tex].
Explanation 2 P(4 or 5):
Multiples of 4 in 1 to 40 are:
There are 10 multiples till 40 (since [tex]4 \times 10 = 40[/tex]) . 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 [tex]5 \times 8 = 40[/tex]). 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,
[tex]P(\text {mult of 4})+P(\text {mult of 5}) -P(\text {mult of 4 and 5})[/tex]
[tex]=\frac{10}{40} +\frac{8}{40} -\frac{2}{40}[/tex]
[tex]=\frac{18}{40} -\frac{2}{40}[/tex]
[tex]=\frac{16}{40}[/tex]
[tex]=\frac{2}{5}[/tex]
So the probability of 4 or 5 is [tex]\frac{2}{5}[/tex].
