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

Question

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 (A) 0.65 (B) 1.46 (C) 1.65 (D) 0.46

Tardigrade Admin · Accepted Answer

P ( E 1)= probability of there is lockdown =0.7 P(E2)= probability of there is lockdown =0.3 A is the event controlled in one month P ( A / E 1)=0.8, P ( A / E 2)=0.3 P(A)=0.7(0.8)+(0.3)(0.3) =0.56+0.09=0.65

$0.65$

$1.46$

$1.65$

$0.46$

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

0.65

1.46

1.65

0.46

P(E1​)= probability of there is lockdown =0.7 P(E2​)= probability of there is lockdown =0.3 A is the event controlled in one month P(A/E1​)=0.8,P(A/E2​)=0.3 P(A)=0.7(0.8)+(0.3)(0.3) =0.56+0.09=0.65

$0.65$

$1.46$

$1.65$

$0.46$

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