Question

A die is thrown once. What is the probability of Cards are marked with numbers 1 to 25 and placed in a box and mixed thoroughly. If one card is drawn at random, find the probability of
a) getting the number 5
b) getting a number less than 11
c) getting a prime number
d) getting a number divisible by 4
e) getting a perfect square.

Answer 1

Answer:

cards bearing the numbers from 1 to 25 are placed in a box,

S={1, 2,3,4.............,25}

therefore n(S) =25

Let the A be the event of getting the number 5

A={5}

therefore, n(A) =1

p(A) =nA) /n(S)

1) p(A) =1/25

2) let B be the Event of getting numbers less than 11

B={1, 2,3,4,,5,6,7,8,9,10}

n(B) =10

p(B) =n(B) /n(S)

p(B) =10/25

p(B) =2/5

3). let c be the Event of getting the prime number.

C={2, 3,5,7,11,13,17,19,23}

n(C)=9

p(C) =n(C) /n(S)

p(C) =9/25

4) let D be the event of getting the numbers divisible by 4

D={4, 8,12,16,20,24}

n(D) =6

p(D) =n(D) /n(S)

p(D) =6/25

5) let E be the event getting the perfect square

E={1, 4,9,16,25}

n(E) =5

p(E) =n(E) /n(S)

p(E) =5/ 25

=1/5

Answer 2

|| ✯✯ QUESTION ✯✯ ||

A die is thrown once. What is the probability of Cards are marked with numbers 1 to 25 and placed in a box and mixed thoroughly. If one card is drawn at random, find the probability of : -

a) Getting the number 5..

b) Getting a number less than 11..

c) Getting a prime number..

d) Getting a number divisible by 4..

e) Getting a perfect square..

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✰✰ ANSWER ✰✰

$Total \:Cards ⟹25$

$\large{\boxed{\bold{\bold{\red{\sf{(a)Getting\:the\:No.\:5}}}}}}$

$⇝<strong>Probability</strong> = \dfrac{No\:of\:fav\:Outcomes}{Total\:no.\:of\:Outcomes}$

☛$Probability = \dfrac{1}{25}$

$\large{\boxed{\bold{\bold{\orange{\sf{(b)Getting\:No.\:less\:than\:11}}}}}}$

$⇝Outcomes =10 ( 1,2,3,4,5,6,7,8,9,10)$

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

☛$Probability =\cancel\dfrac{10}{25}⇝\dfrac{2}{5}$

$\large{\boxed{\bold{\bold{\pink{\sf{(c)Getting\:a\:prime\:No:}}}}}}$

$⇝Outcomes = 9 (2,3,5,7,11,13,17,19,23)$

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

☛$Probability=\dfrac{9}{25}$

$\large{\boxed{\bold{\bold{\green{\sf{(d)Getting\:a\:No\:divisible\:by\:4}}}}}}$

$⇝Outcomes = 6 (4,8,12,16,20,24)$

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

☛$Probability = \dfrac{6}{25}$

$\large{\boxed{\bold{\bold{\purple{\sf{(e)Getting\:a\:Perfect\:Square:}}}}}}$

$⇝Outcomes = 5 (1,4,9,16,25)$

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

☛$Probability = \cancel\dfrac{5}{25}⇝\dfrac{1}{5}$

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Prime Numbers : -

The numbers that are divisible by one and the number itself are known as Prime Numbers. For example 3,7... etc..

Even Numbers : -

The numbers that are divisible by 2 are known as Even numbers. For example 2 , 8... etc..

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