Question

If A and B are two events, such that P(A) = 0.3, P(B) = 0.6 and P (B/A) = 0.5, then
 $P\left( {A \cup B} \right) = $

Answer 1

Hint: This is a question of conditional probability so we have to solve using formulae of conditional probability. We have to understand also P(B/A) means probability of happening of event B when event A has happened. And $P\left( {A \cap B} \right)$ means the probability of happening of both the events A and B simultaneously.

Complete Step-by-Step solution:
We know formulae of conditional probability:
Conditional probability, $P\left( {\dfrac{B}{A}} \right) = \dfrac{{P\left( {A \cap B} \right)}}{{P\left( A \right)}}$
On cross multiplying we get,
$\therefore P\left( {A \cap B} \right) = P\left( {\dfrac{B}{A}} \right) \times P\left( A \right)$
Using the data from given,
$ = 0.5 \times 0.3 = 0.15$
Formulae for probability of either happening of event A or event B will be equal to probability of happening of event A + probability of happening of event B – probability of happening of both the events A and B simultaneously. That is
$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( {A \cap B} \right)$
$
   = 0.3 + 0.6 - 0.15 \\
   = 0.75 \\
 $

Note: Whenever you get this type of question the key concept of solving is we have to understand conditional probability and also remember the formulae of conditional probability and here in this we have to just use the appropriate formula and data from given to get the required answer.