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Questions  >>  CBSE XI  >>  Math  >>  Probability

True-or-False : The probability that a person visiting a zoo will see the giraffee is 0.72,the probability that he will see the bears is 0.84 and the probability that he will see both is 0.52.

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array} $

1 Answer

  • $P(A \cup B)=P(A)+P(B)-P(A \cap B)$
Step 1:
Let us consider that
Probability of a person visiting a zoo and will see a giraffee=P(A)
Probability of a person visiting a zoo and will see a bear=P(B)
Probability of a person visiting both =P$(A\cup B)$
$P(A \cup B)=P(A)+P(B)-P(A \cap B)$
$0.52=0.72+0.84-P(A \cap B)$
Step 2:
$\therefore P(A \cap B)=0.72+0.84-0.52$
$\Rightarrow P(A \cap B)=1.04$
But $P(A \cup B)$ cannot be lesser than $P(A \cap B)$
$\therefore$ The given statement is False.
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