If A and B are two independent events such that P(A)>0.5, P(B)>0.5

Jamya White

Jamya White

Answered question

2023-03-08

If A and B are two independent events such that P ( A ) > 0.5 , P ( B ) > 0.5 , P ( A B ¯ ) = 3 25 P ( A ¯ B ) = 8 25 , then the value of P ( A B ) is
A) 12 25
B) 14 25
C) 18 25
D) 24 25

Answer & Explanation

gelo1368m6

gelo1368m6

Beginner2023-03-09Added 5 answers

The correct answer is A 1225
Given: P ( A B ¯ ) = 3 25 , P ( A ¯ B ) = 8 25
As A and B are independent events, so
P ( A B ) = P ( A ) × P ( B )
Assuming P ( A ) = a , P ( B ) = b
Thus,
P ( A ) P ( A B ) = 3 25
P ( A ) P ( A ) × P ( B ) = 3 25
a a b = 3 25 ( 1 )
P ( B ) P ( A B ) = 8 25
P ( B ) P ( A ) × P ( B ) = 8 25
b a b = 8 25 ( 2 )
From equations (1) and (2), we get
a ( 1 8 25 ( 1 a ) ) = 3 25
a ( 17 25 a ) = 3 ( 1 a )
25 a 2 20 a + 3 = 0
25 a 2 15 a 5 a + 3 = 0
( 5 a 1 ) ( 5 a 3 ) = 0
a = 3 5
( P ( A ) > 0.5 )
From equation (2), we get
P ( A B ) = P ( A ) × P ( B ) = 12 25

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