Question

solve with solution..​

Answer 1

Answer:

(b) 37/45 is the correct option

Step-by-step explanation:

Given :

P(A) = 1/3 ; P(B) = 1/4 ; P(A ∩ B) = 1/5

To Find :

$P(\frac{A'}{B'} )$

Formula :

• P(X) = 1 - P(X')

• P(X ∪ Y) = P(X) + P(Y) - P(X ∩ Y)

• P(X|Y) = $P(\frac{X}{Y} ) = \frac{P(X \cap Y)}{P(Y)}$

• P(A'∩B') = P((A∪B)')

Solution :

So, P(A'|B') = P(A'∩B')/P(B')

P(A∪B) = P(A) + P(B) - P(A∩B)

$=> P(A \cup B) = \frac{1}{3} + \frac{1}{4} - \frac{1}{5} \\\\=> P(A \cup B) = \frac{7}{12} - \frac{1}{5} \\\\=> P(A \cup B) = \frac{23}{60}$

Now,

P((A∪B)') = 1 - P(A ∪ B)

=> $P((A\cap B)') = 1 - \frac{23}{60} = \frac{37}{60}$

So,

P(A'∩B') = P((A∪B)') = 37/60

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

=> P(B') = 1 - 1/4 = 3/4

Now,

$P(\frac{A'}{B'} ) = \frac{P(A' \cap B')}{P(B')}$

$=> P(\frac{A'}{B'} ) = \frac{P(A' \cap B')}{P(B')} = \frac{\frac{37}{60} }{\frac{3}{4} } \\\\=> P(\frac{A'}{B'} ) =\frac{37 \times 4}{ 60 \times 3 } = \frac{37}{45}$

Hope it helps

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