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CBSE Class 12-science Answered

Let there be 'n' people in a room. What is the probability that atleast two people have the same birthday? If another person joins the room, what is the new probability of the above case? What is the value of 'n', for it to be 0.5?
Asked by bjayanta | 04 Sep, 2019, 09:31: PM
answered-by-expert Expert Answer
T h e r e space a r e space n space p e o p l e space i n space t h e space r o o m S o comma space t h e space p r o b a b i l i t y space t h a t space t h e space t w o space p e o p l e space h a v e space t h e space s a m e space b i r t h d a y space i s fraction numerator 365 factorial over denominator left parenthesis 365 minus n right parenthesis factorial 365 to the power of n end fraction A n o t h e r space p e r s o n space j o i n s space t h e space r o o m comma space s o space t h e r e space a r e space n plus 1 space p e o p l e T h e r e f o r e comma space t h e space n e w space p r o b a b i l i t y space i s space fraction numerator 365 factorial over denominator left parenthesis 365 minus left parenthesis n plus 1 right parenthesis right parenthesis factorial 365 to the power of n plus 1 end exponent end fraction equals fraction numerator 365 cross times 364 factorial over denominator left parenthesis 365 minus n minus 1 right parenthesis factorial 365 to the power of n cross times 365 end fraction equals fraction numerator 364 factorial over denominator left parenthesis 364 minus n right parenthesis factorial 365 to the power of n end fraction E q u a t e space fraction numerator 364 factorial over denominator left parenthesis 364 minus n right parenthesis factorial 365 to the power of n end fraction space t o space 0.5 space a n d space t h e n space f i n d space n
Answered by Renu Varma | 05 Sep, 2019, 10:16: AM

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