Question

a die is thrown one find the probability of getting (1)a prime number (2)a number lying between 2 and 5 (3)an even number​

Answer 1

AnswEr :

$\star \sf \: Given\begin{cases} \: \: \: { \bf{Possible \: events = 6 }}\\ \\ \: \: \:{ \bf{No. \: on \: dice = 1,2,3,4,5 \: and \: 6}} \end{cases}$

Now, we know the required formula for finding Probability.

That is,

$\: \: \: \: \star \: \: {\boxed{ \sf{ \purple{Probability = \dfrac{No. \: of \: favourable \: outcomes}{Total \: no. \: of \: favourable \: outcomes}}}}}$

(I) A Prime Number :

• Prime numbers = 2, 3 & 5

• No. of favourable outcomes = 3

$\bigstar \:{ \underline{\sf \: Probability : }} \\ \\ : \implies\sf \: \dfrac{3}{6} \\ \\ : \implies\sf \: \blue{\dfrac{1}{2}}$

(ii) A number lying between 2 and 5 :

• Number's lying between 2 and 5 = 3 & 4

• No. of favourable outcomes = 2

$\bigstar \:{ \underline{\sf \: Probability : }} \\ \\ : \implies\sf \: \dfrac{2}{6} \\ \\ : \implies\sf \: \green{\dfrac{1}{3}}$

(iii) An even number :

• Even numbers = 2, 4 & 6

• No. of favourable outcomes = 3

$\bigstar \: { \underline{\sf \: Probability : }} \\ \\ : \implies\sf \: \dfrac{3}{6} \\ \\ : \implies\sf \: \orange{\dfrac{1}{2}}$