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Probability — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
Question
If $A$ and $B$ be mutually exclusive events associated with a random experiment such that $P(A) = 0.4$ and $P(B) = 0.5,$ then find:
  1. $\text{P}(\text{A}\cup\text{B})$
  2. $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$
  3. $\text{P}(\overline{\text{A}}\cap{\text{B}})$
  4. $\text{P}({\text{A}}\cap\overline{\text{B}})$
✓

Answer

Given,
$P(A) = 0.4$
$P(B) = 0.5$
$\therefore A$ and $B$ are mutually exclusive events, then $\text{P}(\text{A}\cap\text{B})=0$
Now,
  1. $\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A})+\text{P}(\text{B})$
$=0.4+0.5$
$=0.9$
$\therefore\text{P}(\text{A}\cup\text{B})=0.9$
  1. $\text{P}(\overline{\text{A}}\cap\overline{\text{B}})=1-\text{P}(\text{A}\cup\text{B})$
$=1-0.9$
$=0.1$
$\therefore\text{P}(\overline{\text{A}}\cap\overline{\text{B}})=0.1$
  1. $\text{P}(\overline{\text{A}}\cap{\text{B}})=\text{p}(\text{B})-\text{P}({\text{A}}\cap{\text{B}})$
$=0.5-0$
$\therefore\text{P}(\overline{\text{A}}\cap{\text{B}})=0.5$
  1. $\text{P}({\text{A}}\cap\overline{\text{B}})=\text{P}(\text{A})-\text{P}({\text{A}}\cap{\text{B}})$
$=0.4-0$
$=0.4$
$\therefore\text{P}({\text{A}}\cap\overline{\text{B}})=0.4$

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