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CBSE Class 11-science Answered

A test contain 5 questions and each question has 3 choices . A student marks the choices of all the questions randomly . What is the probability that the student has marked at least three questions correctly?
Asked by Kchawla94 | 25 May, 2019, 01:12: AM
answered-by-expert Expert Answer
T h e r e space a r e space 3 space c h o i c e s space f o r space e a c h space q u e s t i o n S o comma space t h e space p r o b a b i l i t y space o f space g e t t i n g space a space c o r r e c t space a n s w e r space i s space 1 third space a n d space g e t t i n g space w r o n g space a n s w e r space i s space 2 over 3 T o space f i n d space t h e space p r o b a b i l t y space t h a t space t h e space s t u d e n t space h a s space m a r k e d space a t space l e a s t space 3 space c o r r e c t space a n s w e r S o comma space t h e space c o r r e c t space a n s w e r s space c a n space b e space 3 comma 4 space o r space 5 P r o b a b i l i t y space o f space g e t t i n g space 3 space c o r r e c t space a n s w e r s space equals space fraction numerator 5 factorial over denominator 3 factorial 2 factorial end fraction open parentheses 1 third close parentheses cubed open parentheses 2 over 3 close parentheses squared P r o b a b i l i t y space o f space g e t t i n g space 4 space c o r r e c t space a n s w e r s space equals space fraction numerator 5 factorial over denominator 4 factorial end fraction open parentheses 1 third close parentheses to the power of 4 open parentheses 2 over 3 close parentheses P r o b a b i l i t y space o f space g e t t i n g space 4 space c o r r e c t space a n s w e r s space equals space open parentheses 1 third close parentheses to the power of 5 T h e r e f o r e comma space t h e space p r o b a b i l t y space t h a t space t h e space s t u d e n t space h a s space m a r k e d space a t space l e a s t space 3 space c o r r e c t space a n s w e r equals fraction numerator 5 factorial over denominator 3 factorial 2 factorial end fraction open parentheses 1 third close parentheses cubed open parentheses 2 over 3 close parentheses squared plus space fraction numerator 5 factorial over denominator 4 factorial end fraction open parentheses 1 third close parentheses to the power of 4 open parentheses 2 over 3 close parentheses plus space open parentheses 1 third close parentheses to the power of 5 equals 1 over 3 to the power of 5 open parentheses 5 cross times 4 cross times 2 plus 5 cross times 2 plus 1 close parentheses equals 51 over 3 to the power of 5
Answered by Renu Varma | 27 May, 2019, 05:06: PM

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