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CBSE Class 12-science Answered

4. The probability that a visitor in the dining room will need the first course is equal to 0.8.  Find the probability that out of 100 visitors, no less than 75 and no more than 90 visitors will order the first dish.
Asked by surajsharmaisonline | 20 Jan, 2023, 12:28: PM
Expert Answer
Probability of ordering the first course by a visitor = 0.8
 
Probability of not ordering the first course by a visitor = 0.2
 
 
Probability p(75) of ordering the first course by exactly 75 visitors out of 100 visitors is
 
p(75) = begin mathsize 14px style C presuperscript 100 subscript 75 space space open parentheses 0.8 close parentheses to the power of left parenthesis 100 minus 75 right parenthesis end exponent left parenthesis 0.2 right parenthesis to the power of 75 end style = begin mathsize 14px style C presuperscript 100 subscript 75 space space open parentheses 0.8 close parentheses to the power of 25 left parenthesis 0.2 right parenthesis to the power of 75 end style
 
Probability p(76) of ordering the first course by exactly 76 visitors out of 100 visitors is
 
p(76) = begin mathsize 14px style C presuperscript 100 subscript 76 space space open parentheses 0.8 close parentheses to the power of left parenthesis 100 minus 76 right parenthesis end exponent left parenthesis 0.2 right parenthesis to the power of 76 end style = begin mathsize 14px style C presuperscript 100 subscript 76 space space open parentheses 0.8 close parentheses to the power of 24 left parenthesis 0.2 right parenthesis to the power of 76 end style
 
Similarly for 77, 78, ...............................90 visitors
.
.
.
.
.
 
Probability p(90) of ordering the first course by exactly 90 visitors out of 100 visitors is
 
p(90) = begin mathsize 14px style C presuperscript 100 subscript 90 space space open parentheses 0.8 close parentheses to the power of left parenthesis 100 minus 90 right parenthesis end exponent left parenthesis 0.2 right parenthesis to the power of 90 end style = begin mathsize 14px style C presuperscript 100 subscript 90 space space open parentheses 0.8 close parentheses to the power of 10 left parenthesis 0.2 right parenthesis to the power of 90 end style

 
probability of not less than 75 visitors and not greater than 90 visitors out of 100 visitors is
 
begin mathsize 14px style p left parenthesis space 75 space less or equal than space x space less or equal than space 90 space right parenthesis space equals space sum from x equals 75 to 90 of C presuperscript 100 subscript x space left parenthesis 0.8 right parenthesis to the power of left parenthesis 100 minus x right parenthesis end exponent space left parenthesis 0.2 right parenthesis to the power of x end style
 

 
Answered by Thiyagarajan K | 21 Jan, 2023, 10:15: AM

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CBSE 12-science - Maths
4. The probability that a visitor in the dining room will need the first course is equal to 0.8.  Find the probability that out of 100 visitors, no less than 75 and no more than 90 visitors will order the first dish.
Asked by surajsharmaisonline | 20 Jan, 2023, 12:28: PM
ANSWERED BY EXPERT
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