# Three persons PQ and R independently try to hit a target.  If the probabilities of their hitting the target are    respectively, then the probability that the target is hit by P or Q but not by R is : Option 1) Option 2) Option 3) Option 4)

As we learnt in

$P\left ( A\cup B \right )= P\left ( A \right )+P\left ( B \right )-P\left ( A\cap B \right )$

in general:

$P\left ( A_{1}\cup A_{2}\cup A_{3}\cdots A_{n} \right )=\sum_{i=1 }^{n}P\left ( A_{i} \right )-\sum_{i< j}^{n}P\left ( A_{i}\cap A_{j} \right )+\sum_{i< j< k}^{n} P\left ( A_{i}\cap A_{j}\cap A_{k} \right )-\cdots -\left ( -1 \right )^{n-1}P\left ( A_{1}\cap A_{2}\cap A_{3}\cdots \cap A_{n} \right )$

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Independent events -

Two or more events are said to be independent if occurence or non occurence of any of them does not affect the probability of occurence of or non - occurence of other events.

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$P(P)=\frac{3}{4};P(Q)=\frac{1}{2};P(R)=\frac{5}{8}$

$P(P\ or\ Q)=P(P)+P(Q)-P(P\cap Q)$

$=\frac{3}{4}+\frac{1}{2}-\frac{3}{8}$

$=\frac{7}{8}$

$P(\bar{R})=\frac{3}{4}$

P (P or Q not R) =$\frac{7}{8}\times \frac{3}{8}=\frac{21}{16}$

Option 1)

This is correct

Option 2)

This is incorrect

Option 3)

This is incorrect

Option 4)

This is incorrect

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