A fair coin is tossed 10 times. Let p be the probability of getting a head in the hird trial (but not before) and let q be the probability of getting the head after the second trial (but not in the first two trials) then `p/q` is very close to a)`1/4` b) `1/2` c) 2 d) 4

A fair coin is tossed 10 times. Let p be the probability of getting a

1.	A fair coin is tossed 10 times. Let p be the probability of getting a head in the hird trial (but not before) and let q be the probability of getting the head after the second trial (but not in the first two trials) then `p/q` is very close to a)`1/4` b) `1/2` c) 2 d) 4
Answer» Here. `p` is the probability of getting a head in third trial. It means, first two trials will be tails and third trial will be head. `:. p = P(T)P(T)P(H) = 1/21/21/2 = 1/8` Now, `q` is the probability of getting heads after two trials. It can be heads after two trials, third trials and so on. `:. q = (1/21/21/2)+(1/21/21/21/2)+(1/21/21/21/21/2)+...(1/21/21/21/21/21/21/21/21/21/2*)` `=> q = 1/8+1/16+...1/1024` It is a `G.P.` with first term, `a = 1/8` and common ratio, `r = 1/2` with total terms `8`. `:. q = 1/8((1-(1/2)^8)/(1-1/2))` `:. p/q = (1/8)/(1/8((1-(1/2)^8)/(1-1/2)))` `=>p/q = (1-1/2)/(1-1/256) = (1/2)/(255/256) = 128/255` So, `p/q` is close to `1/2`.

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A fair coin is tossed 10 times. Let p be the probability of getting a head in the hird trial (but not before) and let q be the probability of getting the head after the second trial (but not in the first two trials) then `p/q` is very close to a)`1/4` b) `1/2` c) 2 d) 4

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