There are 4 different scenarios in which he will "hit his target".rajataga wrote:A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
A. 1
B. 255/256
C. 175/256
D. 1/4
E. 1/2
S1: hit once, miss 3 times
S2: hit twice, miss twice
S3: hit 3 times, miss once
S4: hit all 4 times
One way we could answer this question is to calculate the probability of each scenario and add them together.
However, a much quicker way to answer the question is to recognize that there's only 1 scenario we do NOT want: miss all 4 times. We can use our trusty "one minus" probability formula:
Prob(want) = 1 - Prob(don't want)
So, the probability of missing all 4 is:
3/4 * 3/4 * 3/4 * 3/4 = 81/256
Therefore, the probability of hitting at least one target is:
1 - 81/256 = 175/256... choose (C).
