Let A and B be two events such that (P ( A ) = 0.3)and (P (... | MATH - USE OF PERMUTATIONS AND COMBINATIONS IN PROBABILITY | SolveeIt

Let A and B be two events such that $P ( A ) = 0.3$ and

$P ( A \cup B ) = 0.8$ . If A and B are independent events, then

$P ( B ) =$

$\frac { 5 } { 6 }$

$\frac { 5 } { 7 }$

$\frac { 3 } { 5 }$

$\frac { 2 } { 5 }$

Answer

$\frac { 5 } { 7 }$

Explanation

Here $P ( A \cup B ) = 0.8$ , $P ( A ) = 0.3$ and A and B are

independent events.

Let $P ( B ) = x$ . $\therefore$ $P ( A \cup B ) = P ( A ) + P ( B ) - P ( A \cap B )$

Ž $P ( A \cup B ) = P ( A ) + P ( B ) - P ( A ) \cdot P ( B )$

Ž $0.8 = 0.3 + x - 0.3 x$ Ž $x = \frac { 5 } { 7 }$ .

Question: Let *A* and *B* be two events such that \(P ( A ) = 0.3\)and \(P ( A \cup B ) = 0.8\). If *A* and *...