please-help-me-solve-these-two-questions-1-A-magician-cuts-a-rope-into-two-parts-at-a-point-selected-at-random-what-is-the-probability-that-the-length-of-the-longer-rope-is-at-least-8-times-

Question Number 50299 by OTCHRRE ABDULLAI last updated on 15/Dec/18

p l e a s e h e l p m e s o l v e t h e s e t w o

q u e s t i o n s

1 . A m a g i c i a n c u t s a r o p e i n t o t w o

p a r t s a t a p o i n t s e l e c t e d a t

r a n d o m . w h a t i s t h e p r o b a b i l i t y t h a t

t h e l e n g t h o f t h e l o n g e r r o p e i s a t l e a s t

8 t i m e s t h e l e n g t h o f t h e s h o r t e r

r o p e .

2 . f i n d t h e s u m o f c o - e f f i c i e n t o f

t h e b i n o m i a l e x p a n s i o n o f

{(4 x - 1)}^{16}

Commented by OTCHRRE ABDULLAI last updated on 16/Dec/18

p l e a s e s i r i h a d t h e p r o b a b i l i t y t o b e

1 - \frac{5}{9} = 0.444

u s i n g a n i d e a f r o m y o u r d i a g r a m

p l e a s e c h e c k f o r m e s i r

Commented by Abdo msup. last updated on 15/Dec/18

w e h a v e {(4 x - 1)}^{16} = \sum_{k = 0}^{16} C_{16}^{k} {(4 x)}^{k} {(- 1)}^{16 - k}

= \sum_{k = 0}^{16} C_{16}^{k} {(- 4)}^{k} x^{k} \Rightarrow s u m o f c o e f f i c i e n t i s

= \sum_{k = 0}^{16} C_{16}^{k} {(- 4)}^{k} = {(- 4 + 1)}^{16} = 3^{16} .

Commented by mr W last updated on 16/Dec/18

t o A b d u l l a i s i r :

n o w y o u c a n a l s o s o l v e i f t h e q u e s t i o n

i s “ w h a t i s t h e p r o b a b i l i t y t h a t t h e

l e n g t h o f t h e l o n g e r r o p e i s a t l e a s t

6 t i m e s b u t a t m o s t 9 t i m e s o f t h e

s h o r t e r {r o p e}^{″} . c a n y o u g i v e i t a t r y ?

Commented by OTCHRRE ABDULLAI last updated on 16/Dec/18

T h a n k y o u v e r y m u c h m y b o s s

G o d b l e s s y o u

Commented by OTCHRRE ABDULLAI last updated on 16/Dec/18

i w i l l s i r

Commented by mr W last updated on 16/Dec/18

n o s i r! t r y t o d r a w a d i s g r a m w h i c h

s h o w s t h e a r e a s w h e r e t h e c u t c a n b e

p l a c e d a n d t h e n c a l c u l a t e t h e s u m o f

t h e s e a r e a s . t h e f r a c t i o n o f t h e s e a r e a s

i s t h e r e s u l t .

t h e r e s u l t s h o u l d b e \frac{3}{35}, i t h i n k .

Commented by OTCHRRE ABDULLAI last updated on 16/Dec/18

o k s i r t h a n k s

Answered by mr W last updated on 15/Dec/18

(1)

1 - \frac{7}{9} = \frac{2}{9} \approx 0.222

(2)

S u m . o f a l l c o e f . = {(4 \times 1 - 1)}^{16} = 3^{16}

Commented by mr W last updated on 15/Dec/18

Commented by OTCHRRE ABDULLAI last updated on 15/Dec/18

T h i s m a n i s g r e a t

p l e a s e c a n y o u a d d e x p l a n a t i o n t o

q u e s t i o n 1 f o r m e

Commented by mr W last updated on 15/Dec/18

w h e n t h e c u t i s i n t h e r e d a r e a, t h e

l e n g t h o f t h e l o n g e r p a r t i s l e s s t h a n

t h e 8 t i m e s o f t h e s h o r t e r p a r t, t h i s

p r o b a b i l i t y i s 7 / 9 .

w h e n t h e c u t i s i n t h e g r e e n a r e a s, t h e

l e n g t h o f t h e l o n g e r p a r t i s a t l e a s t

8 t i m e s o f t h e s h o r t e r p a r t, t h i s

p r o b a b i l i t y i s 1 - 7 / 9 = 2 / 9 = 0.222

Commented by Cheyboy last updated on 15/Dec/18

Thank alot Sir I have learn from it .

Commented by OTCHRRE ABDULLAI last updated on 15/Dec/18

I n f a c t m r W y o u a r e g r e a t G o d b l e s s y o u

Commented by mr W last updated on 15/Dec/18

t h a n k s a l o t s i r s!

Commented by peter frank last updated on 15/Dec/18

yeah true he is among of best

solver in this forum i real appriciate him and GOD bless him