Question

If \[P(S) = 0.3\],\[P(T) = 0.4\]and S,T are independent events. Then find the value of \[P(\dfrac{S}{T})\].
A. \[0.2\]
B. \[0.3\]
C. \[0.4\]
D. \[0.12\]

Answer 1

Hint: In order to solve the question, first write the formula for conditional probability. Then, find the intersection of the independent events. Finally, substitute the given values to find the required answer.

Formula used:
The formula for conditional probability is
\[P\left( {\dfrac{A}{B}} \right) = \dfrac{{P\left( {A \cap B} \right)}}{{P(B)}}\]
If A and B are independent event, then
\[P\left( {A\cap B} \right) = P(A) \times P(B)\]

Complete step-by-step solution :
Given that
\[P(S) = 0.3\]
\[P(T) = 0.4\]
Here it is asked to find the value of \[P(\dfrac{S}{T})\].
We can write that
\[P\left( {\dfrac{S}{T}} \right) = \dfrac{{P\left( {S \cap T} \right)}}{{P(T)}}\]
Here since S and T are independent events, we can write that
\[P\left( {S \cap T} \right) = P(S) \times P(T)\]
That is
\[P\left( {\dfrac{S}{T}} \right) \]
\[= \dfrac{{P\left( S \right) \times P(T)}}{{P(T)}}\]
\[ = \dfrac{{0.3 \times 0.4}}{{0.4}}\]
\[ = 0.3\]
Hence option B is the correct answer.

Additional information:
Conditional probability is the probability of an event occurring given that another event has already happened.
The conditional probability formula is applied on two events such that the events are neither independent nor mutually exclusive.
The formula of conditional probability \[P\left( {\dfrac{A}{B}} \right) = \dfrac {{P\left({A\cap B}\right)}}{{P(B)}}\].

Note: Students can make mistakes while writing the formula of conditional probability. Remember that conditional probability means the probability that an event occur when other events has already occurred. Also, students can get confused between the intersection of independent and dependent events.