Question

if a number x is choosen at random from the numbers-3,-2,-1,0,1,2,3 . what is the probability that
${x }^{2} \leqslant 4$
​

Answer 1

Answer:

We will check square of each number given above, that whose value comes ≤ 4

⠀

• (- 3)² = (- 3 × - 3) = 9⠀
• (- 2)² = (- 2 × - 2) = 4⠀
• (- 1)² = (- 1 × - 1) = 1⠀
• ( 0 )² = (0 × 0) = 0⠀
• ( 1 )² = (1 × 1) = 1⠀
• ( 2 )² = (2 × 2) = 4⠀
• ( 3 )² = (3 × 3) = 9⠀

⠀

We seen that Square of - 2, - 1 , 0, 1, 2 are either equal to or less than 4.

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf P(E)=\dfrac{Number\:of\:events}{Total\:number\:of\:events}\\\\\\:\implies\sf P(E) = \dfrac{5}{7}\\\\\\:\implies\sf P(E) = 0.71$

⠀

$\therefore\:\underline{\textsf{Hence, probability of getting x ^\text2 \leqslant 4 is \textbf{0.71}}}.$

$\rule{200}{1}$

FACTS :

• Probability of any event falls b/w 0 and 1

• 0 indicates uncertainty of event, while 1 indicates certainty of event

• 0 ≤ P(E) ≤ 1

• P(E) + P(not E) = 1

Answer 2

Answer:

We will check square of each number given above, that whose value comes ≤ 4

⠀

(- 3)² = (- 3 × - 3) = 9⠀

(- 2)² = (- 2 × - 2) = 4⠀

(- 1)² = (- 1 × - 1) = 1⠀

( 0 )² = (0 × 0) = 0⠀

( 1 )² = (1 × 1) = 1⠀

( 2 )² = (2 × 2) = 4⠀

( 3 )² = (3 × 3) = 9⠀

⠀

We seen that Square of - 2, - 1 , 0, 1, 2 are either equal to or less than 4.

\underline{\bigstar\:\textsf{According to the given Question :}}

★According to the given Question :

\begin{gathered}:\implies\sf P(E)=\dfrac{Number\:of\:events}{Total\:number\:of\:events}\\\\\\:\implies\sf P(E) = \dfrac{5}{7}\\\\\\:\implies\sf P(E) = 0.71\end{gathered}

:⟹P(E)=

Totalnumberofevents

Numberofevents

:⟹P(E)=

7

5

:⟹P(E)=0.71

⠀

\therefore\:\underline{\textsf{Hence, probability of getting x$^\text2 \leqslant $ 4 is \textbf{0.71}}}.∴

Hence, probability of getting x

2

⩽ 4 is 0.71

.

\rule{200}{1}

FACTS :

• Probability of any event falls b/w 0 and 1

• 0 indicates uncertainty of event, while 1 indicates certainty of event

• 0 ≤ P(E) ≤ 1

• P(E) + P(not E) = 1

Sitting and phone chalaying.. xD

wbu?