Question

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)

Answer 1

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 $\frac{2}{5}$.