We have the following probabilities:

$$\bullet$$ The probability that the target is hit by the person P is $${3 \over 4}$$.

$$\bullet$$ The probability that the target is not hit by the person P is $$1 - {3 \over 4} = {1 \over 4}$$.

$$\bullet$$ The probability that the target is hit by the person Q is $${1 \over 2}$$.

$$\bullet$$ The probability that the target is not hit by the person Q is $$1 - {1 \over 2} = {1 \over 2}$$.

$$\bullet$$ The probability that the target is hit by the person R is $${5 \over 8}$$.

$$\bullet$$ The probability that the target is not hit by the person R is $$1 - {5 \over 8} = {3 \over 8}$$.

Here, we have used the fact that if the probability of occurrence of an event is p, then the probability of non-occurrence of an event is $$q = 1 - p$$.

Therefore, the probability that the target is hit by P or Q and not by R is

(Probability that the target is hit by P and not by Q and R) + (Probability that the target is hit by Q and not by P and R) + (Probability that the target is hit by both P and Q and not by R)

$$ = \left( {{3 \over 4}} \right)\left( {{1 \over 2}} \right)\left( {{3 \over 8}} \right) + \left( {{1 \over 4}} \right)\left( {{1 \over 2}} \right)\left( {{3 \over 8}} \right) + \left( {{3 \over 4}} \right)\left( {{1 \over 2}} \right)\left( {{3 \over 8}} \right)$$

$$ = {9 \over {64}} + {3 \over {64}} + {9 \over {64}} = {{9 + 3 + 9} \over {64}} = {{21} \over {64}}$$