A letter of English alphabet is chosen at random. Find the probability that the chosen word (1) comes in the word TRIGONOMETRY and (2) does not comes in the word TRIGONOMETRY.

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Solution

Dear Student,

$L e t t e r s i n t h e w o r d t r i g o n o m e t r y = {T, R, I, G, O, N, M, E, Y} = 9 L e t t e r s i n t h e E n g l i s h A l p h a b e t = 26 P r o b a b i l i t y = \frac{F a v o u r a b l e o u t c o m e s}{T o t a l n u m b e r o f o u t c o m e s} (1) P r o b a b i l i t y t h a t t h e l e t t e r c o m e s i n t r i g o n o m e t r y = \frac{9}{26} (2) P r o b a b i l i t y t h a t t h e l e t t e r d o e s n o t c o m e i n t r i g o n o m e t r y = 1 - P r o b a b i l i t y t h a t t h e l e t t e r c o m e s i n t r i g o n o m e t r y = 1 - \frac{9}{26} = \frac{26 - 9}{26} = \frac{17}{26}$

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