Question

The odds in favour, of standing first of three students Amit, Vikas and Vivek appearing at an examination are 1:2.2: 5 and 1 :7. respectively. What is the probability that either of them' will stand firs t (assume that a tie for the first place is not possible)

Answer 1

The odds (in favor) of an event or a proposition is the ratio of the probability that the event will happen to the probability that the event will not happen

So, required probability = P(First person standing first) + P(Second person standing first) + P(Third person standing first)

= 1/(1+2) + 2/(2+5) + 1/(1+7)

= 1/3 + 2/7 + 1/8

= (56 + 48 + 21)/168

= 125/168

Comments

 1/(1+2) + 2/(2+5) + 1/(1+7)

why did u add 1,2,1 to denominators of I,II& III person probability respectively ?

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Because probability is the ratio of chance of favorable case to TOTAL cases and total includes fav + unfav.

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You just add the three probabilitues but when u  take prob. Of A standing first then why u didnt multiply prob. Of B & C not standing first ...similarly as in case of B & C standing first ???

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because in question it is mentioned that tie is not possible.

so in one person’s favors it is considered that anyone other cannot stand first in that case

 i hope you get the answer