Question

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?

Answer 1

Probability that A hits the target = 1/3

Probability that B hits the target = 2/3

Probability that C hits the target = 1

The expected number of shots is not fixed, it can be within a range.

So let's calculate the number of shots following the procedure

(1) A fires in the air.

(2) B shoots C.

(3) A shoots B.

Total number of shots fired = 3

(1) A fires in the air.

(2) B misses C.

(3) C shoots B.

(4) A shoots C.

Total number of shots fired = 4

(1) A fires in the air.

(2) B misses C.

(3) C shoots B.

(4) A misses C.

(5) C shoots A.

Total number of shots = 5

So we can expect the number of shots fired until only one person is left = 3 to 5 shots