Question

numbers of 1 to 50 are printed on marbles and mixed. if one marble is drawn at random,what is the the probability of
1)a prime number
2)an even number
3)a number divisible by 5 ​

Answer 1

ANSWER

Total no: of outcomes = 50

$\boxed{\boxed{\bold{SOMETHING \ YOU \ NEED \ TO \ KNOW}}}}}$

${\bold{Probability \ of \ an \ event} = \dfrac{\bold{Total \ no: \ of \ given \ event}}{\bold{Total \ no: \ of \ outcomes}}$

1) Probability of a prime number

Sample space = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,

Total no: of prime numbers = 15

${\bold{Probability \ of \ a \ prime \ number} = \dfrac{\bold{Total \ no: \ of \ prime \ numbers}}{\bold{Total \ no: \ of \ outcomes}}$

$= \dfrac{15}{50} = {\boxed{\boxed{\bold{\dfrac{3}{10}}}}$

2) Probability of an even number

Total no: of even numbers = 25

${\bold{Probability \ of \ an \ even \ number} = \dfrac{\bold{Total \ no: \ of \ even \ numbers}}{\bold{Total \ no: \ of \ outcomes}}$

$=\dfrac{25}{50} = \boxed{\boxed{\bold{\dfrac{1}{2} }}}}$

3) Probability of a number divisible by 5

Sample space: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Total no: of numbers divisible by 5 = 10

${\bold{Probability \ of \ a \ number \ divisible \ by \ 5} = \dfrac{\bold{Total \ no: \ of \ numbers}}{\bold{Total \ no: \ of \ outcomes}}$

$\implies \dfrac{10}{50} = \boxed{\boxed{\bold{\dfrac{1}{5} }}}}$

                                                 

Answer 2

Answer:

1) 3/10

2) 1/2

3) 1/5

Step-by-step explanation:

Given that numbers of 1 to 50 are printed on marbles and mixed. Here, the total number of marbles is 50. And one marble is drawn at random. We need to find out the probability of a marble that it is:

1)a prime number

2)an even number

3)a number divisible by 5

Now,

$\boxed{\underline{\sf{ \purple{Probability=\dfrac{Number\:of\: favourable\: outcomes}{Total\: number\:of\: outcomes}}}}}$

Probability is denoted by "P".

(Total number of outcomes = Total number of marbles = 50)

1) a prime number

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47. There are total 15 prime numbers between 1 to 50. So, here the number of favourable outcomes is 15.

P(prime number) = 15/50 = 3/10

$\rule{70mm}{2pt}$

2) an even number

Numbers which are divisible by 2 are considered as even numbers. And out of 50 marbles which are marked 1 to 50, half of them are even number. (50/2 = 25)

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32 34, 36, 38, 40, 42, 44, 46, 48 and 50. Therefore, the number of favourable outcomes is 25. So,

P(even number) = 25/50 = 1/2

$\rule{70mm}{2pt}$

3) a number divisible by 5

The numbers that are divisible by 5 from 50 marbles marked 1 to 50 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. OR

Divide the total number of marbles by 5 to get that number of marbles that are divisible by 5. So, 50/5 = 10. Here, the number of favourable outcomes is 10.

P(number divisible by 5) = 10/50 = 1/5