Question

card marked with the number 2 to 101 are placed in a box and mixed thoroughly. One card is drown from this box , find the probability that tha number of the card is . (a) an even number , (b) a number less then 14. , (c) a number which is a perfect square. , (d) a prime number less then 20.​

Answer 1

$\large\underline{\bold{Given- }}$

• Card marked with the number 2 to 101 are placed in a box.

• One card is taken out randomly from the box.

$\large\underline{\sf{To\:Find - }}$

• (a) an even number

• (b) a number less than 14

• (c) a number which is a perfect square

• (d) a prime number less than 20.

$\begin{gathered}\Large{\sf{{\underline{Formula \: Used - }}}}  \end{gathered}$

$\sf \:Probability \: of \: an \: event =\dfrac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes \: in \: sample \: space}$

$\large\underline{\sf{Solution-}}$

Given that

Cards number from 2 to 100 are in the box,

it implies, there are 100 cards in the box and one card can be taken out in 100 ways.

• So, total number of outcomes = 100.

$\large\underline{\sf{Answer (a)- }}$

From 2 to 101,

• The even numbers are 2, 4, 6, _ _ _ _, 100.

• It implies, there are 50 even numbers.

So,

• Total number of favourable outcomes are 50.

Hence,

$\sf \:Probability \: of \: getting \: even \: number =\dfrac{50}{100} = \dfrac{1}{2}$

$\large\underline{\sf{Answer (b)- }}$

From 2 to 101,

Cards bearing number less than 14 are 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

• It implies, there are 12 cards bearing number less than 14.

So,

• Total number of favourable outcomes are 12.

Thus,

$\sf \:Probability \: of \: getting \: \: number \: < 14 =\dfrac{12}{100} = \dfrac{3}{25}$

$\large\underline{\sf{Answer (c)- }}$

From 2 to 101, the numbers which are perfect squares are 4, 9, 16, 25, 36, 49, 64, 81, 100

• It means these are squares of 9 cards having number 2, 3, 4, 5, 6, 7, 8, 9, 10

So,

• Total number of favourable outcomes are 9.

Hence,

$\sf \:Probability \: of \: getting \: perfect \: square \: number =\dfrac{9}{100}$

$\large\underline{\sf{Answer (d)- }}$

From 2 to 101, prime number less than 20 are 2, 3, 5, 7, 11, 13, 17, 19.

• It implies, there are 8 prime numbers less than 20

So,

• Total number of favourable outcomes are 8.

Thus,

$\sf \:Probability \: of \: getting \:prime \: number < 20=\dfrac{8}{100} = \dfrac{2}{25}$

Additional Information :-

Explore more :-

• The sample space of a random experiment is the collection of all possible outcomes.

• An event associated with a random experiment is a subset of the sample space.

• The probability of any outcome is a number between 0 and 1.

• The probability of sure event is 1.

• The probability of impossible event is 0.

• The probabilities of all the outcomes add up to 1.

• The probability of any event A is the sum of the probabilities of the outcomes in A.