Question

the tickets marked 4 to 34 are put in a box after well mixing them. A ticket is removed from the box. find the probability that the no. marked on the tickets is:
(I) prime numbers
(II) an odd number which is a perfect square
(iii)a number divisible by 5​

Answer 1

Answer:

Solution(i):

Let E be the event of drawing a number from the cards numbered from 11 to 60

Odd numbers from 11 to 60=11,13,15,.....,89

No. of favorable outcomes=25

Total no. of possible outcomes =50

We know that , probability

$= \frac{(no \: of \: favorable \: outcomes)}{total \: number \: of \: possible \: outcomes)\: } = \frac{25}{50} = \frac{1}{2}$

Therefore, the probability of an odd number from the cards numbered 11 to 60

$= \frac{1}{2}$

Solution(ii):

Let F be the event of drawing a perfect square number from the cards numbered from 11 to 60

Perfect square numbers from 11 to 60=16,25,36,49

No. of favorable outcomes=4

Total no. of possible outcomes =50

We know that, Probability P(F) 

$= \frac{no \: of \: favourable \: outcomes \: }{totl \: number \: of \: possible \: outcomes} = \frac{4}{50} = \frac{2}{25}$

Therefore, the probability of drawing a perfect square number from the cards numbered from 11 to 60

$= \frac{2}{25}$

Solution(iii):

Let G be the event of drawing a number divisible by 5 from the cards numbered from 11 to 60

Numbers divisible by 5 from 11 to 60=15,20,25,30,35,40,45,50,55,60

No. of favorable outcomes=10

Total no. of possible outcomes =50

We know that, Probability P(G) =

$\frac{no \: of \: favourable \: outcomes \: }{totl \: number \: of \: possible \: outcomes \: } = \frac{10}{50} = \frac{1}{5}$

Therefore, the probability of drawing a number divisible by 5 from the cards numbered from 11 to 60

$= \frac{1}{5}$

Solution(iv):

Let H be the event of drawing a prime number less than 20 from the cards numbered from 11 to 60

Prime numbers less than 20 from 11 to 60=11,13,17,19

No. of favorable outcomes=4

Total no. of possible outcomes =50

We know that, Probability P(H) 

$= \frac{no \: of \: favourble \: outcomes}{total \: number \: of \: possible \: outcomes \: } = \frac{4}{50} = \frac{2}{25}$

Therefore, the probability of drawing a prime number less than 20 from the cards numbered from 11 to 60

$= \frac{2}{25}$