Question

a box contain 90 discs which are numbered from 1 to 90. If one discs is drawn at random from the box. Find the probability that it bears a two digit number, a perfect square number, a number divisible by 5, a prime number less than 30​

Answer 1

Step-by-step explanation:

Given :-

A box contain 90 discs which are numbered from 1 to 90. If one discs is drawn at random from the box.

To find :-

Find the probability that it bears

1)a two digit number

2)a perfect square number

3)a number divisible by 5

4)a prime number less than 30

To find :-

Given that

The number of discs in the box = 90

Total number of all possible outcomes = 90

Probability of getting a two digits number :-

The two digits numbers are starting from 10,11,..90

Number of two digit numbers = 90-9 = 81

Number of favourable outcomes = 81

We know that

Probability of an event E is P(E)

=Number of favourable outcomes/ Total number of all possible outcomes

=> Probability of getting a perfect square number

=>81/90

=> 9/10

Probability of getting a perfect square number :-

The perfect square numbers are 1,4,9,16,25,36,49,64,81

Number of perfect square numbers = 9

Number of favourable outcomes = 9

We know that

Probability of an event E is P(E)

=Number of favourable outcomes/ Total number of all possible outcomes

=> Probability of getting a perfect square number

=>9/90

=> 1/10

Probability of getting a number divisible by 5 :-

The numbers divisible by 5 are 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90

Number of the number divisible by 5 = 18

Number of favourable outcomes = 18

We know that

Probability of an event E is P(E)

=Number of favourable outcomes/ Total number of all possible outcomes

=> Probability of getting a number divisible by 5

=>18/90

=> 1/5

Probability of getting a prime number less than 30 :-

The prime numbers less than 30 are 2,3,5,7,11,13,17,19,23,29

Number of prime numbers less than 30 = 10

Number of favourable outcomes = 10

We know that

Probability of an event E is P(E)

=Number of favourable outcomes/ Total number of all possible outcomes

=> Probability of getting a prime number less than 30

=>10/90

=> 1/9

Answer :-

1) Probability of getting a two digits number = 9/10

2)Probability of getting a perfect square number = 1/10

3)Probability of getting a number divisible

by 5 =1/5

4)Probability of getting a prime number less than 30 = 1/9

Used formulae:-

→ Probability of an event E is P(E)

=Number of favourable outcomes/ Total number of all possible outcomes

Answer 2

Answer:

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