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p-a-or-b-0-7-and-p-a-0-4-find-p-b-if-a-and-b-are-independent-




Question Number 186547 by ali009 last updated on 05/Feb/23
p(a or b)=0.7 and p(a)=0.4  find p(b) if a and b are independent
$${p}\left({a}\:{or}\:{b}\right)=\mathrm{0}.\mathrm{7}\:{and}\:{p}\left({a}\right)=\mathrm{0}.\mathrm{4} \\ $$$${find}\:{p}\left({b}\right)\:{if}\:{a}\:{and}\:{b}\:{are}\:{independent} \\ $$
Answered by som(math1967) last updated on 06/Feb/23
p(aorb)=p(a)+p(b)−p(a  and b)  .7=.4+p(b)−.4p(b)  ⇒.6p(b)=.3  p(b)=0.5
$${p}\left({aorb}\right)={p}\left({a}\right)+{p}\left({b}\right)−{p}\left({a}\:\:{and}\:{b}\right) \\ $$$$.\mathrm{7}=.\mathrm{4}+{p}\left({b}\right)−.\mathrm{4}{p}\left({b}\right) \\ $$$$\Rightarrow.\mathrm{6}{p}\left({b}\right)=.\mathrm{3} \\ $$$${p}\left({b}\right)=\mathrm{0}.\mathrm{5} \\ $$

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