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PROBABILITY — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPROBABILITY1 Mark
MCQ
Choose the correct answer. If $A$ and $B$ are mutually exclusive events, then:
  • ✓
    $\text{P(A)}\leq\text{P}(\bar{\text{B}})$
  • B
    $\text{P(A)}\geq\text{P}(\bar{\text{B}})$
  • C
    $\text{P}(\text{A})<\text{P}(\bar{\text{B}})$
  • D
    none of these.
✓

Answer

Correct option: A.
$\text{P(A)}\leq\text{P}(\bar{\text{B}})$
For mutually exclusive events,
$\text{P}(\text{A}\cap\text{B})=0$
$\therefore\ \text{P}(\text{A}\cup\text{B})=\text{P(A)}+\text{P(B)}$ $\big[\because\text{ P}(\text{A}\cap\text{B})=0\big]$
$\Rightarrow\text{P}(\text{A})+\text{P(B)}\leq1$
$\Rightarrow\text{P(A)}+1-\text{P}(\bar{\text{B}})\leq1$ $\big[\text{P(B)}=1-\text{P}(\bar{\text{B}})\big]$
$\Rightarrow\text{P(A)}-\text{P}(\bar{\text{B}})\leq0$
$\Rightarrow\text{P(A)}-\text{P}(\bar{\text{B}})$

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