Please solve the following question:
 

Asked by manasd | 25th Dec, 2016, 07:28: PM

Expert Answer:

begin mathsize 16px style N o t e colon space H o w space m a n y space b u l b s space a r e space d r a w n space f o r m space l o t space i s space n o t space g i v e n space i n space q u e s t i o n.
A s s u m i n g space t h a t space i t space i s space 4 comma space s o l u t i o n space i s space p r o v i d e d.
L e t space X space b e space t h e space n u m b e r space o f space d e f e c t i v e space b u l b s space i n space 4.
H e n c e comma space X space equals space 0 comma space 1 comma space 2 comma space 3 space o r space 4
N u m b e r space o f space d e f e c t i v e space b u l b s equals 5
N u m b e r space o f space g o o d space b u l b s equals 20
rightwards double arrow T o t a l space n u m b e r space o f space b u l b s equals 20 plus 5 equals 25
P left parenthesis X equals 0 right parenthesis equals P left parenthesis N o space D e f e c t i v e space b u l b right parenthesis equals fraction numerator C presuperscript 20 subscript 4 over denominator C presuperscript 25 subscript 4 end fraction equals fraction numerator 20 cross times 19 cross times 18 cross times 17 over denominator 25 cross times 24 cross times 23 cross times 22 end fraction equals 969 over 2530
P left parenthesis X equals 1 right parenthesis equals P left parenthesis 1 space D e f e c t i v e space b u l b space a n d space 3 space G o o d space b u l b s space right parenthesis equals fraction numerator C presuperscript 5 subscript 1 cross times C presuperscript 20 subscript 3 over denominator C presuperscript 25 subscript 4 end fraction equals 1140 over 2530
P left parenthesis X equals 2 right parenthesis equals P left parenthesis 2 space D e f e c t i v e space b u l b s space a n d space 2 space G o o d space b u l b s space right parenthesis equals fraction numerator C presuperscript 5 subscript 2 cross times C presuperscript 20 subscript 2 over denominator C presuperscript 25 subscript 4 end fraction equals 380 over 2530
P left parenthesis X equals 3 right parenthesis equals P left parenthesis 3 space D e f e c t i v e space b u l b s space a n d space 1 space G o o d space b u l b space right parenthesis equals fraction numerator C presuperscript 5 subscript 3 cross times C presuperscript 20 subscript 1 over denominator C presuperscript 25 subscript 4 end fraction equals 40 over 2530
P left parenthesis X equals 4 right parenthesis equals P left parenthesis A l l space D e f e c t i v e space b u l b s space right parenthesis equals fraction numerator C presuperscript 5 subscript 4 over denominator C presuperscript 25 subscript 4 end fraction equals 1 over 2530
T h u s comma space T h e space p r o b a b i l i t y space d i s t r i b u t i o n space o f space t h e space r a n d o m space v a r i a b l e space X space i s space a s space f o l l o w s colon
X colon space space space space space space space space space space space space space space space space space space space space space space space space space space space 0 space space space space space space space space space space space space space space space space space space space space space 1 space space space space space space space space space space space space space space space space space space space space space 2 space space space space space space space space space space space space space space space space space space space space space 3 space space space space space space space space space space space space space space space space space space space space space 4
P left parenthesis X equals 0 right parenthesis space space space space space space space space space space space space space 969 over 2530 space space space space space space space space space space space space space 1140 over 2530 space space space space space space space space space space space space space 380 over 2530 space space space space space space space space space space space space space 40 over 2530 space space space space space space space space space space space space space 1 over 2530 end style

Answered by Rashmi Khot | 26th Dec, 2016, 10:07: AM

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