20th sum plz

Asked by lovemaan5500 | 8th Oct, 2019, 09:43: PM

Expert Answer:

p is the probability that a man aged x dies in a year
T h e r e space a r e space n space m e n space A subscript 1 comma space A subscript 2 comma... space A subscript n
L e t space E subscript i space b e space t h e space e v e n t space t h a t space a space m a n space A subscript i space w i l l space d i e space i n space a space y e a r space w h e r e space i equals 1 comma 2 comma... comma n
S u p p o s e space n o n e space o f space t h e m space d i e s space i n space a space y e a r
T h e r e f o r e comma space p r o b a b i l i t y space t h a t space n o n e space o f space t h e m space d i e s space
space space space space space space space space space space space space space space space space space equals left parenthesis 1 minus P left parenthesis E subscript 1 right parenthesis right parenthesis left parenthesis 1 minus P left parenthesis E subscript 2 right parenthesis right parenthesis.... left parenthesis 1 minus P left parenthesis E subscript n right parenthesis right parenthesis
space space space space space space space space space space space space space space space space space equals left parenthesis 1 minus p right parenthesis left parenthesis 1 minus p right parenthesis... left parenthesis 1 minus p right parenthesis equals left parenthesis 1 minus p right parenthesis to the power of n space P r o b a b i l i t y space t h a t space a t space l e a s t space o n e space o f space t h e m space d i e s space i n space a space y e a r
equals 1 minus left parenthesis 1 minus p right parenthesis to the power of n space N o w comma space p r o b a b i l i t y space o f space d y i n g space A subscript 1 space a m o n g space n space m e n space equals 1 over n
T h e r e f o r e comma
p r o b a b i l i t y space t h a t space A subscript 1 space w i l l space b e space t h e space f i r s t space t o space d i e space i n space a space y e a r equals 1 over n times open square brackets 1 minus left parenthesis 1 minus p right parenthesis to the power of n close square brackets

Answered by Renu Varma | 9th Oct, 2019, 11:00: AM