The-probability-that-athlete-will-win-a-race-is-1-6-and-that-he-will-be-second-and-third-are-1-4-and-1-3-respectively-what-is-the-probability-that-he-will-not-be-first-in-the-first-three-place-

Question Number 152683 by rexford last updated on 31/Aug/21

T h e p r o b a b i l i t y t h a t a t h l e t e w i l l w i n a r a c e i s \frac{1}{6} a n d t h a t

h e w i l l b e s e c o n d a n d t h i r d a r e \frac{1}{4} a n d \frac{1}{3}

r e s p e c t i v e l y . w h a t i s t h e p r o b a b i l i t y t h a t h e w i l l n o t b e f i r s t

i n t h e f i r s t t h r e e p l a c e!

P l e a s e, h e l p m e o u t

Answered by Olaf_Thorendsen last updated on 31/Aug/21

P (X ⩽ 3) = P (X = 1) + P (X = 2) + P (X = 3)

P (X ⩽ 3) = \frac{1}{6} + \frac{1}{4} + \frac{1}{3} = \frac{2 + 3 + 4}{12} = \frac{5}{6}