- Home
- Standard 11
- Mathematics
14.Probability
easy
An unbiased die is thrown twice. Let the event $A$ be 'odd number on the first throw' and $B$ the event 'odd number on the second throw '. Check the independence of the events $A$ and $B$.
Option A
Option B
Option C
Option D
Solution
If all the $36$ elementary events of the experiment are considered to be equally likely, we have
$P(A)=\frac{18}{36}=\frac{1}{2}$ and $P(B)=\frac{18}{36}=\frac{1}{2}$
Also $P(A \cap B)=P($ odd number on both throws $)$
$=\frac{9}{36}=\frac{1}{4}$
Now $\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})=\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}$
Clearly $\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\mathrm{P}(\mathrm{A}) \times \mathrm{P}(\mathrm{B})$
Thus, $A$ and $B$ are independent events
Standard 11
Mathematics
