Question

when a die is thrown find the probability of following getting prime number getting not a prime number getting a number greater than 4​

Answer 1

$\huge{\underline{\bf\red{Questi {\mathbb{O}} n} :}}$

$\sf When \: a \: die \: is \: thrown, \: find \\ \sf the \: probability \: of \: getting : \\ (i) \sf \: a \: prime \: number \qquad \\ (ii) \sf \: not \: a \: prime \: number \\ (iii) \sf \: a \: no. \: greater \: than \: 4$

$\huge{\underline{\: \bf\green{Answ {\mathbb{E}} r}\ \: :}}$

• $(i) \quad \dfrac{1}{2}$

• $(ii) \quad \dfrac{1}{2}$

• $(iii) \quad \dfrac{1}{3}$

$\Large{\underline{\bf\purple{Giv {\mathbb{E}} n}\ :}}$

• Total possible outcomes = 6

$\Large{\underline{\bf\purple{We \ Kn {\mathbb{O}} w}\ :}}$

• no. of Prime Nos. from 1 to 6 on a die = 3 [ i.e.: 2, 3 & 5 ]

• no. of Nos. which are not prime b/w 1 & 6 = 3 [ i.e.: 1, 4 & 6 ]

• no. of Nos. greater than 4 = 2 [ i.e.: 5 & 6 ]

$\Large{\underline{\bf\purple{To \ Fi {\mathbb{N}} d}\ :}}$

• $\boxed{ \rm probability}$

$\huge{\underline{\bf\blue{Soluti {\mathbb{O}} n}\ :}}$

$\underline{ \bf \underline{ \blue{option} \: \red{(i)}}}$

$\begin{aligned} \sf P(getting \: a \: prime \: no.)& = \sf \frac{no. \: of \: prime \: nos.}{total \: no. \: of \: outcomes} \\ \\ & = \frac{3}{6} = \cancel{ \frac{3}{6} }_{2} \\ \\ & = \frac{1}{2} & & & & & & & \end{aligned}$

$\underline{ \bf \underline{ \blue{option} \: \red{(ii)}}}$

$\begin{aligned} \sf P(not \: getting \: a \: prime \: no.)& = \sf \frac{no. \: of \: not \: primes}{total \: no. \: of \: outcomes} \\ \\ & = \frac{3}{6} = \cancel{ \frac{3}{6} }_{2} \\ \\ & = \frac{1}{2} & & & & & & & \end{aligned}$

$\underline{ \bf \underline{ \blue{option} \: \red{(iii)}}}$

$\begin{aligned} \sf P(getting \: a\: no. > 4)& = \sf \frac{no. \: of \: nos. > 4}{total \: no. \: of \: outcomes} \\ \\ & = \frac{2}{6} = \cancel{ \frac{2}{6} }_{3} \\ \\ & = \frac{1}{3} & & & & & & & \end{aligned}$

$\red{\rule{5.5cm}{0.02cm}}$

$\purple{\rule{7.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$