Shooters A and B start shooting alternatively at the target (A starts first). The probability that A hits the target is p, while it is q for B (the outcomes of all the attempts are independent). Whoever hits the target first is the winner. What is the probability of A winning
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'3_ Shooters A, B, and C are having a truel The probability that A hits his target is 1/3, the probability for B is 2/3, and the probability for C is 1. A goes first; then B, then C, etc. until only one shooter is left_ Suppose that A shoots into the air for his first shot, then B shoots at C, and C, if still alive, shoots at B. What is the expected number of shots fired until the truel is over?'
Kirsty G.
One shot is fired form each of three guns. Let $A, B, C$ denote the events that the target is hit by the first, second and the third gun respectively. Assuming that $A, B, C$ are mutually independent events and the $P(A)=0.5, P(B)=0.6$, $P(C)=0.8$, find the probability that at least on hit is registered.
Manisha S.
An athlete is shooting arrows at a target. She has a record of hitting the centre $30 \%$ of the time. Find the probability that she hits the centre a) with her second shot b) exactly once with her first three shots c) at least once with her first three shots.
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