Question

A die is rolled and two events A and B are defined as follows.
A: An odd number turns up
B: A prime Number turns up

Find the value of 36 P$(A\cup B)$.

Answer 1

we will use the result P$(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$ to find the answer in the first method.

P(A) = P(an odd number) = $\frac{3}{6}=\frac{1}{2}$

similarly,P(B) = P$\left(\right\{2,3,5\left\}\right)=\frac{1}{2}$

P(A intersection B) =P$\left(\right\{3,5\left\}\right)$

=$\frac{2}{6}$

=$\frac{1}{3}$

$\Rightarrow P(A\cup B)$ = $\frac{1}{2}+\frac{1}{2}-\frac{1}{3}$

=$1-\frac{1}{3}$

=$\frac{2}{3}$

In the second method,we will find the set $A\cup B$ and find P$(A\cup B)$

$A\cup B$ =$\left\{numberswhichareprimeorodd\right\}$

=$\{1,2,3,5,\}$

$\Rightarrow P(A\cup B)$ =P$\left(\right\{1,2,3,5,\left\}\right)$

= $\frac{4}{6}$

=$\frac{2}{3}$

$\Rightarrow$ Answer =$36\times \frac{2}{3}$

=24