5-integers-are-selected-randomly-from-Z-what-is-the-probability-that-at-least-one-of-them-is-divisible-by-5-

Question Number 3927 by prakash jain last updated on 24/Dec/15

5 integers are selected randomly from Z^{+}

what is the probability that at least one

of them is divisible by 5 .

Commented by prakash jain last updated on 26/Dec/15

\frac{1}{5} is the probability of one integer being

divisible by 5 .

Probablity of at least one integer being

divisible by 5 = 1 - all not divisible by 5 .

= 1 - {(\frac{4}{5})}^{5}

Commented by Filup last updated on 26/Dec/15

y e s t h a t i s w h a t i m e a n t

Commented by Filup last updated on 26/Dec/15

Every 1 in 5 sequencial values are

devisibly by 5 .

e . g . 7, 8, 9, 10, 11

n, x \in Z^{+}

S = {5, 10, 15, \dots}

P (x \in S) = \frac{1}{5}

This could be horribly wrong

i have a s s u m e d 0 \notin Z^{+}

Commented by Rasheed Soomro last updated on 26/Dec/15

I f o n e i n t e g e r w e r e t o b e s l e c t e d t h e n ?

Commented by Rasheed Soomro last updated on 26/Dec/15

I t h i n k \frac{1}{5} i n c a s e y o u s e l e c t o n e i n t e g e r

o u t o f i n t e g e r s! O f c o u r s e i t e g e r s a r e i n f i n i t e

b u t t h e n u m b e r o f t y p e s w r t d i v i s i b i l i t y b y 5

i s f i n i t e

I n t e g e r s (m o d 5) w i t h r e m a i n d e r 0

I n t e g e r s (m o d 5) w i t h r e m a i n d e r 1

I n t e g e r s (m o d 5) w i t h r e m a i n d e r 2

I n t e g e r s (m o d 5) w i t h r e m a i n d e r 3

I n t e g e r s (m o d 5) w i t h r e m a i n d e r 4

Commented by Filup last updated on 26/Dec/15

Y e s . O n l y i f i n t e g e r .

I t is out of Z^{+}

If it were out of R^{+} (or R),

the probabilty would be \frac{1}{\infty} = 0 % .

B e c a u s e there are infinitly less integers

than non - i n t e g e r s

Facebook Tweet Pin