Question

(IV) a number less than 9?
A die is thrown once. Find the probability of getting
(1) a prime number; (ii) a number lying beiween 2 and 6;​

Answer 1

Answer:

(1) 1/2

(2) 1/2

Step-by-step explanation:

Given : A dice is thrown once.

(1) Total number of outcomes = 6 {1, 2, 3, 4, 5, 6}

Favourable outcomes of getting a prime number = 3 {2, 3, 5}

P(x) = Favourable outcomes / Total outcomes

P(getting a prime number) = 3/6 = 1/2

(2) Total number of outcomes = 6 {1, 2, 3, 4, 5, 6}

Favourable outcomes of getting a number lying between 2 and 6 = 3 {3, 4, 5}

P(x) = Favourable outcomes / Total outcomes

P(getting a number lying between 2 and 6) = 3/6 = 1/2

• Probability means possibility.
• Deals with the occurence of the random event.

Answer 2

$\bf{\Huge{\boxed{\tt{\red{ANSWER\::}}}}}$

$\bf{\Large{\underline{\sf{Given\::}}}}}$

A die is thrown once.

$\bf{\Large{\underline{\bf{To\:find\::}}}}$

The probability of getting;

• A prime number.
• A number lying between 2 & 6.

$\bf{\Large{\underline{\rm{\pink{Explanation\::}}}}}$

We know that formula of the Probability:

$\leadsto\tt{\orange{Probability\:\:P(E)\:=\:\frac{Number\:of\:favorable\:outcomes}{Total\:possibles\:outcomes.} }}$

$\bf{\Large{\boxed{\bf{First\:Case\::}}}}}$

Total outcomes that can be 1, 2, 3, 4, 5, 6.

$\mapsto\sf{Number\:of\:possible\:outcomes\:of\:a\:die\:=\:6}$

A/q

$\longmapsto\rm{Prime\:number\:on\:a\:die\:=\:2\:,\:3\:,\:\&\:5}$

$\longmapsto\rm{Total\:prime\:number\:on\:a\:die\:=\:3}$

$\longmapsto\sf{P(E)\:\:=\frac{Number\:of\:outcomes(prime\:number\:comes)}{Total\:number\:of\:outcomes}}$

$\longmapsto\sf{P(E)\:\:=\frac{3}{6} }$

$\longmapsto\sf{P(E)\:\:=\cancel{\frac{3}{6} }}$

$\longmapsto\sf{\blue{P(E)\:\:=\frac{1}{2} }}$

$\bf{\Large{\boxed{\bf{Second\:Case\::}}}}}$

$\longmapsto\sf{Number\:lying\:between\:2\:\:\&\:\:6\:in\:die.}$

$\longmapsto\sf{Number\:lying\:\:=\:\:3\:\:,\:\:4\:\:,\:\:5}$

$\longmapsto\sf{Total\:Number\:lying\:=3}$

Therefore,

$\longmapsto\tt{P(E)\:\:=\:\:\frac{Number\:lying\:between\:2\:and\:6}{Total\:number\:outcomes\:in\;a\:die}}$

$\longmapsto\tt{P(E)\:\:=\:\:\frac{3}{6} }$

$\longmapsto\tt{P(E)\:\:=\:\:\cancel{\frac{3}{6} }}$

$\longmapsto\tt{\blue{P(E)\:\:=\:\:\frac{1}{2} }}$