If A and B be mutually exclusive events associated with a random … - Vidyadip

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:

$\text{P}(\text{A}\cup\text{B})$
$\text{P}(\overline{\text{A}}\cap\overline{\text{B}})$
$\text{P}(\overline{\text{A}}\cap{\text{B}})$
$\text{P}({\text{A}}\cap\overline{\text{B}})$

✓

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,

$\text{P}(\text{A}\cup\text{B})=\text{P}(\text{A})+\text{P}(\text{B})$

$=0.4+0.5$
$=0.9$
$\therefore\text{P}(\text{A}\cup\text{B})=0.9$

$\text{P}(\overline{\text{A}}\cap\overline{\text{B}})=1-\text{P}(\text{A}\cup\text{B})$

$=1-0.9$
$=0.1$
$\therefore\text{P}(\overline{\text{A}}\cap\overline{\text{B}})=0.1$

$\text{P}(\overline{\text{A}}\cap{\text{B}})=\text{p}(\text{B})-\text{P}({\text{A}}\cap{\text{B}})$

$=0.5-0$
$\therefore\text{P}(\overline{\text{A}}\cap{\text{B}})=0.5$

$\text{P}({\text{A}}\cap\overline{\text{B}})=\text{P}(\text{A})-\text{P}({\text{A}}\cap{\text{B}})$

$=0.4-0$
$=0.4$
$\therefore\text{P}({\text{A}}\cap\overline{\text{B}})=0.4$

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