Answer to Question #194315 in Statistics and Probability for Ezra

Question

Two fair dice are tossed simultaneously and the bigger of the two numbers obtained is recorded. If A represent the event 'bigger number is 4' and B represents the event 'bigger number is odd', find:

a.) P(A)

b.) P(A U B)

Answer 1

$A\to$ Bigger number is 4

(i) Sample sapce for A is {$(1,4),(2,4),(3,4),(4,1),(4,2),(4,3)$ }

So, $P(A)=\dfrac{6}{36}=0.166$

(ii) $B\to$ Bigger number is odd

So, $P(B)=\dfrac{10}{36}=0.27$

$P(A\cap B)=0$

Hence, $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

$=0.166+0.27-0\\=0.436$