Gate Exam Numerical Ability Probability

A fair coin is tossed infinite times then find the probability of 4th head occurs
exactly at 10th times.

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Gate Other Question

A woman with four children bought a sack of peanuts. To the oldest child, a boy she gave one peanut and 1/4th of what remained, and to each of the other children she did the same. The second child was a girl, the third a boy and the last a girl. It was found that the boys had received 100 more peanuts than the girls. What was the initial number of peanuts? A person having three coins, first coin have both sides head, second coin
and third coin having one head and one tail. If one coin is picked up randomly
and tossed then the probability that it shows head having tail is...