Question

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4. ​

Answer 1

${\huge\fbox\pink{♥}\fbox\blue{A}\fbox\purple{N}\fbox\green{S}\fbox\red{W}\fbox\orange{E}\fbox{R}\fbox\gray{♥}}$

Multiples of 3 & 4 are 12, 24, 36, 48, i.e., 4 nos.

P(a multiple of 3 and 4) = 4/50=2/5

Answer 2

$\Large{\underbrace{\underline{\bf{QUESTION\:}}}}:$

A number is selected at random from first 50 natural numbers. Find the probability that it is a multiple of 3 and 4.

$\Large{\underbrace{\underline{\bf{ANSWER\:}}}}:$

${\bf{Given\::}}$

• A number is selected at random from the first 50 natural numbers.

$\\ {\bf{To\: Find\::}}$

• The probability that it is a multiple of 3 & 4.

$\\ {\bf{Solution\::}}$

$:\implies\:\tt\red{Total\:no.\:of\: possible\: outcomes\:\atop{=\:50\:,i.e.\:[1, 2, 3, .... 50]\:}}$

✯ First of all we will find the multiple of 3 from 1 to 50, are

➛ 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48

✯ Now, we will find the multiple of 4 from 1 to 50, are

➛ 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48

✯ Now, we have to find the number such that it is multiple of 3 and 4. So, we will find the multiples that are common to both 3 and 4, that are

➛ 12, 24, 36, 48

Hence,

$:\implies\:\tt\blue{No.\:of\: favourable\: outcomes\:\atop{=\:4\:,i.e.\:[12, 24, 36, 48]\:}}$

As we know that,

✯ Probability of an event to happen [P(E)] is given as,

$\orange\bigstar\:\mid\:\bf\purple{P(E)\:=\:\dfrac{No.\:of\: favourable\: outcomes}{Total\:no.\:of\: possible\: outcomes}\:}\:\mid\:\green\bigstar$

➟ P(E) = $\tt{\dfrac{4}{50}\:}$

➟ P(E) = $\bf\green{\dfrac{2}{25}\:}$