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! Please,help me out


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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

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