Question

A two digit number is written down at random. What is the probability that it: (a) is divisible by 5; (b) is divisible by 3; (c) is greater than 50; (d) is a square number?

Answer 1

Given :

• A two digit number is written randomly.

To Find :

• Probability

Solution :

As we're given that a two digit number is given as randomly. So, we know that total two digits numbers will be : 90

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(1) Probability that the number is divisible by 5 .

And there are 90/5 = 18 numbers which are divisible by 5

⇒Probability = No. of Outcomes/Total

⇒Probability = 18/90

⇒Probability = 6/30

⇒Probability = 1/5

$\therefore$ Probability that number is divisible by 5 is 1/5

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(b) Divisible by 3

There are total, 90/3 = 30 numbers which are divisible by 3

⇒Probability = 30/90

⇒Probability = 3/9

⇒Probability = 1/3

$\therefore$ Probability that number is divisible by 3 is 1/3

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(c) Number is greater than 50

There are total , 90 - 50 = 40 two digit numbers which are greater than 50

⇒Probability = 40/90

⇒Probability = 4/9

$\therefore$ Probability that number is greater than 50 is 4/9

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(d) Number is a square number

Total two digit number which is a square number are : 16,25,36,49,64,81

So, in total 6 numbers

⇒Probability = 6/90

⇒Probability = 1/15

$\therefore$ Probability that number is a square number is 1/15

Answer 2

✯✯ QUESTION ✯✯

A two digit number is written down at random. What is the probability that it: (a) is divisible by 5; (b) is divisible by 3; (c) is greater than 50; (d) is a square number?

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✰✰ ANSWER ✰✰

$\implies\tt{Total\:Two\:digit\:Numbers=90}$

1.Is divisible by 5

$\implies\tt{Favourable\:Outcomes=18}$

$\implies\tt{Probability=\dfrac{No.\:of\:fav.\:Outcomes}{Total\:no.\:of\:Outcomes}}$

$\implies\tt{\cancel\dfrac{18}{90}}$

$\implies\tt{\small{\boxed{\bold{\bold{\orange{\sf{\dfrac{1}{5}}}}}}}}$

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2.Is divisible by 3

$\implies\tt{Favourable\:Outcomes=30}$

$\implies\tt{Probability=\dfrac{No.\:of\:fav.\:Outcomes}{Total\:no.\:of\:Outcomes}}$

$\implies\tt{\cancel\dfrac{30}{90}}$

$\implies\tt{\small{\boxed{\bold{\bold{\pink{\sf{\dfrac{1}{3}}}}}}}}$

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3.Is Greater than 50

$\implies\tt{Favourable\:Outcomes=40}$

$\implies\tt{Probability=\dfrac{No.\:of\:fav.\:Outcomes}{Total\:no.\:of\:Outcomes}}$

$\implies\tt{\cancel\dfrac{40}{90}}$

$\implies\tt{\small{\boxed{\bold{\bold{\red{\sf{\dfrac{4}{9}}}}}}}}$

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4.Is a square number

$\implies\tt{Favourable\:Outcomes=6}$

$\implies\tt{Probability=\dfrac{No.\:of\:fav.\:Outcomes}{Total\:no.\:of\:Outcomes}}$

$\implies\tt{\cancel\dfrac{6}{90}}$

$\implies\tt{\small{\boxed{\bold{\bold{\red{\sf{\dfrac{1}{15}}}}}}}}$