Question

 If A and B are events of a random experiment such that P(AUB) = 4/5 , P( A’UB’) = 7/10 , P(B) = 2/5 then P(A) equals : *

1 point

(A) 9/10

(B) 8/10

(C) 7/10

(D) 3/5

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Answer 1

Answer:

option c - 7/10

Step-by-step explanation:

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Answer 2

Given:

P(A U B) = 4/5

P($\bar{A}$ U $\bar{B}$ ) = 7/10

P(B) = 2/5

To find:

P(A) = ?

Calculation:

We know the formula

P(A U B) = P(A) + P(B) - P(A ∩ B)  ……(1)

From the given data

$\Rightarrow P(\bar A \cup \bar B) = \frac{7}{10}\\ \\\Rightarrow P(\bar A \ \bar{\cap}\ \bar B) = \frac{7}{10}$

The sum of probabilities = 1

$\Rightarrow P(A \cap B) +(\bar A \ \bar{\cap}\ \bar B) = 1\\ \\\Rightarrow P(A \cap B) = 1 - \frac{7}{10}\\ \\\Rightarrow P(A \cap B) = \frac{3}{10}$

From equation(1)

=> P(A U B) = P(A) + P(B) - P(A ∩ B)

    (4/5) = P(A) + (2/5) - (3/10)

    (4/5) - (2/5) + (3/10) = P(A)  

    P(A) = (3/10) + (2/5)

    P(A) = 7/10

   $\boxed{P(A) = \frac{7}{10} }$