Question

Card with number 1,2,3,---------------100 are placed in a and mixed thoroughly one card is drawn what is the probability that is 1. Prime number less than 30 2. Perfect square number. 3 . A multi of 5or 7

Answer 1

Total number of cards=100

1)prime numbers which are less than 30 are

=2,3,5,7,11,13,17,19,23,29.

So, total prime numbers which are less than 30 is 10

So required probability =10/100=1/10

2)Perfect square numbers are 1,4,9,16,25,36,49,56,81,100

Total perfect square are 10.

So required probability = 10/100=1/10

3)Multiple of 5 or 7 are 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,7,14,21,28,42,49,56,63,70,77,84,91,98

Total multiple of 5 or 7 is 33

So required probability is 33/100

Hope it helped .......

Answer 2

$\bold{Given}$

Cards are numbered from 1 -100 and mixed .A card is drawn randomly so we need to find :-

TOTAL CONDITION = 100

◼$\bold{Prime \: number \: less \: than \: 30}$

FAVOURABLE CONDITION =10 {2,3,5,7,11,13,17,19,23,29}

$\boxed{PROBABLITY = \dfrac{FAVOURABLE \: CONDITION}{TOTAL \: CONDITION}}$

$PROBABLITY =\dfrac{10}{100}$

$\boxed{PROBABLITY =\dfrac{1}{10}}$

◼$\bold{PERFECT \: SQUARE}$

FAVOURABLE CONDITION = 10

={1,4,9,16,25,36,49,64,81,100}

$\boxed{PROBABLITY = \dfrac{FAVOURABLE \: CONDITION}{TOTAL \: CONDITION}}$

$PROBABLITY =\dfrac{10}{100}$

$\boxed{PROBABLITY =\dfrac{1}{10}}$

◼$\bold{A \: multiple \: of \:5 \: or \: 7}$

MULTIPLE OF 5 ={5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100}

MULTIPLE OF 7 ={7,14,21,28,35,42,49,56,63,70,77,84,91,98}

70 and 35 is repeated twice ,it will be counted as one

FAVOURABLE CONDITIONS = 32

$\boxed{PROBABLITY = \dfrac{FAVOURABLE \: CONDITION}{TOTAL \: CONDITION}}$

$PROBABLITY =\dfrac{32}{100}$

$\boxed{PROBABLITY =\dfrac{8}{25}}$