KCET · Maths · Probability
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 1.65
- C 1.46
- D 0.46
Answer & Solution
Correct Answer
(A) 0.65
Step-by-step Solution
Detailed explanation
Let event \(E_1=\) There is a lockdown,
Event \(E_2=\) There is no lockdown,
and \(A=\) Pandemic is controlled in one month
Now, \(P\left(E_1\right)=0.7, P\left(E_2\right)=0.3\),
\(P\left(A \mid E_1\right)=0.8\) and \(P\left(A \mid E_2\right)=0.3\)
\(P(A)=0.7(0.8)+0.3(0.3)=0.56+0.09=0.65\)
Event \(E_2=\) There is no lockdown,
and \(A=\) Pandemic is controlled in one month
Now, \(P\left(E_1\right)=0.7, P\left(E_2\right)=0.3\),
\(P\left(A \mid E_1\right)=0.8\) and \(P\left(A \mid E_2\right)=0.3\)
\(P(A)=0.7(0.8)+0.3(0.3)=0.56+0.09=0.65\)
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