A can hit a target 3 times in 5 shots, B 2 item in 5 shots, C 3 times in 4 shots They fire a volley. What is the probability that 2 shots hit?

Question: A can hit a target 3 times in 5 shots, B 2 item in 5 shots, C 3 times in 4 shots They fire a volley. What is the probability that 2 shots hit?

Solution:

Fire a volley means that A, B and C all try to hit the target simultaneously. Twp shots hit the target in one of the following ways:
(a) A and B hit and C fails to hit.
(b) A and C hit and B fails to hit.
(c) B and C hit and A fails to hit.

The chance of hitting by A = 3/5 and of not hitting by him = 1- 3/5=2/5
The chance of hitting by B = 2/5 and of not hitting by him = 1- 2/5=3/5
The chance of hitting by C = 3/4 and of not hitting by him = 1- 3/4=1/4
The probability of (a) = 3/5 x 2/5 x 1/4 = 6/100
The probability of (b) = 3/5 x 3/4 x 3/5 = 27/100
The probability of (c) = 2/5 x 3/4 x 2/5 = 6/100

Since (a), (b) and (c) are mutually exclusive events, the probability that two shots hit
6/100 + 27/100 + 12/100 = 45/100 = 9/20 or 9/20 x 100 = 45%

The classical or a prior probability measures have two very interesting characteristics. First, the objects referred to as fair coins true dice or fair deck of cards are abstractings in the sense that no real world object exactly possesses the features postulated. Secondly, in order to determine the probabilities, no coins had to be tossed, no dice rolled nor cards shuffled. That is no experimental data were required to be collected; the probability calculations were based entirely on logical prior (thus a priori) reasoning. It may be possible that the results of a few trials of an experiment may be different than the expected on the basis of probability. If a coin is tossed 10 times, it may be that head may turn up 7 times and tail 3 times whereas, according to the prior probability the head should turn 5 times and tail also 5 times. But in 500 or 1000 trials, the results may be much nearer to the probable results.