Question

Numbers 2 to 21 are written on different cards. Find the probability that card will have a prime number. Give me full solution

Answer 1

⚝ Given :-

• cards marked with numbers from 2 to 21.

⚝ To Find :-

• The probability that card will have a prime number.

⚝ Solution :-

➦ Prime number 2 to 21 = 2, 3, 5, 7, 11, 13, 17, 19

➦ Number of Favourable outcome = 8

➦ Total Number of outcomes = 20

• We know that :

$\pmb{ \underline{ \boxed{ \sf{ \pink{ Probability \: P(E) = \frac{Total \: no. \: of \: possible \: outcomes)}{(No. \: of \: favorable \: outcomes)} }}}}}$

Now,

$\hookrightarrow{ \sf{Probability \: = \frac{8}{20} }}$

$\hookrightarrow{ \sf{Probability \: = \cancel\frac{8}{20} }}$

$\hookrightarrow{ \sf{Probability \: = \frac{2}{5} }}$

Henceforth, the required probability of getting a prime number is $\sf{ \frac{2}{5} }$

_____________________

• What is prime number ?

→ A Number that can be divided exactly only by itself and 1 is called Prime Number.

→ Example - 2, 3, 5, etc...

Answer 2

"Question given:

• Numbers 2 to 21 are written on different cards. Find the probability that card will have a prime number.

Information provided with us:

• Numbers 2 to 21 are written on different cards.

What we have to calculate:

• We have to calculate and find out the probability of that card which would have a prime number

Concept:

• Here the concept of probability is going to be implemented. Probability is typically something which may or may not happen. In the formula of probability E denotes the event. In this question we would first find out the number of favourable outcomes, total outcomes and then substitute the values and solve it.

Using Formula:

• $\red{ \boxed{ \bf{P (E) \: = \: \dfrac{Number \: of \: favourable \: outcomes }{Total \: possible \: outcomes} }}}$

Here,

• P is the probability
• E is the event

Performing Calculations:

• As we know there are total 8 prime numbers from 2 to 21.

$\therefore \: \small\underline{\bf{Total \: number \: of \: favourable \: outcomes \: would \: be </p><p> \: 8}}$

• The total no of favourable outcomes is 20. It can be even checked by start counting from 2 to 21.

Substituting the values in the formula,

$: \longmapsto \: \tt{Probability \: = \: \dfrac{8}{20} }$

$: \longmapsto \: \tt{Probability \: = \: \dfrac{ \cancel{8}}{ \cancel{20}} }$

$: \longmapsto \: \tt{Probability \: = \: \dfrac{4}{10}}$

$: \longmapsto \: \tt{Probability \: = \: \dfrac{ \cancel4}{ \cancel10}}$

$: \longmapsto \: \bigstar\underline{\boxed{\tt{Probability \: = \: \dfrac{2}{5}}}} \bigstar$"