If A and B are two independent events such that P( barA)=0.75, P(A ∪ B)=0.65, and P ( B )=x, then find the value of x :

Question

If A and B are two independent events such that P( barA)=0.75, P(A ∪ B)=0.65, and P ( B )=x, then find the value of x : (A) (5/14) (B) (9/14) (C) (8/15) (D) (7/15)

Tardigrade Admin · Accepted Answer

P ( A )=(1/4), P ( B )=(3/4), P ( A ∪ B )=(13/20) (1/4)+ x -(1/4) ⋅ x =(13/20) (3/4) x-(13/20)-(5/20)=(8/20) x=(8/20) × (4/3)=(8/15)

Q. If $A$ and $B$ are two independent events such that $P (\overset{ˉ}{A}) = 0.75, P (A \cup B) = 0.65$ , and $P (B) = x$ , then find the value of $x$ :

$\frac{5}{14}$

$\frac{9}{14}$

$\frac{8}{15}$

$\frac{7}{15}$

$P (A) = \frac{1}{4}, P (B) = \frac{3}{4}, P (A \cup B) = \frac{13}{20}$
$\frac{1}{4} + x - \frac{1}{4} \cdot x = \frac{13}{20}$
$\frac{3}{4} x - \frac{13}{20} - \frac{5}{20} = \frac{8}{20}$
$x = \frac{8}{20} \times \frac{4}{3} = \frac{8}{15}$

Q. If A and B are two independent events such that P(Aˉ)=0.75,P(A∪B)=0.65, and P(B)=x, then find the value of x :

145​

149​

158​

157​