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  4. A pandemic has been spreading all over the world. The probabilities are 0.7 that there will be a lockdown, 0.8 that the pandemic is controlled in one month if there is a lockdown and 0.3 that it is controlled in one month if there is no lockdown. The probability that the pandemic will be controlled in one month is

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Q. A pandemic has been spreading all over the world. The probabilities are $0.7$ that there will be a lockdown, $0.8$ that the pandemic is controlled in one month if there is a lockdown and $0.3$ that it is controlled in one month if there is no lockdown. The probability that the pandemic will be controlled in one month is

KCETKCET 2022Probability - Part 2

Solution:

$P \left( E _{1}\right)=$ probability of there is lockdown $=0.7$
$P\left(E_{2}\right)=$ probability of there is lockdown $=0.3$
$A$ is the event controlled in one month
$P \left( A / E _{1}\right)=0.8, P \left( A / E _{2}\right)=0.3$
$P(A)=0.7(0.8)+(0.3)(0.3) $
$=0.56+0.09=0.65$