P, Q, R try to hit a target independently with probabilities 34,12,58.

Question

P, Q, R try to hit a target independently with probabilities $\dfrac34,\dfrac12,\dfrac58$. Find the probability the target is hit by P or Q but not R.

Accepted Answer

$$P = [P(P)+P(Q)-P(P)P(Q)]\times(1-P(R)) = \left(\frac34+\frac12-\frac38\right)\times\frac38 = \frac78\times\frac38=\frac{21}{64}$$

Solutions · 1