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

Explanation

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) = 1/2*1/2*1/2 = 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 = (1/2*1/2*1/2)+(1/2*1/2*1/2*1/2)+(1/2*1/2*1/2*1/2*1/2)+...(1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*1/2*)`

`=> 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`.

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