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 $36P(A\cup B)$.

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

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