Aspire Faculty ID #17305 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

If $A$ and $B$ are two independent events with  
$P(A)=\frac{3}{5}$ and $P(B)=\frac{4}{9}$, then

$P(A' \cap B')$ is equal to

Solution

Since $A$ and $B$ are independent,

$P(A\cap B)=P(A)P(B)$

Now

$P(A') = 1 - P(A)$  
$P(B') = 1 - P(B)$

So

$P(A') = 1-\frac{3}{5}=\frac{2}{5}$

$P(B') = 1-\frac{4}{9}=\frac{5}{9}$

For independent events, complements are also independent.

Hence

$P(A'\cap B') = P(A')P(B')$

$=\frac{2}{5}\times\frac{5}{9}$

$=\frac{2}{9}$
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