Question

Two different dice are tossed together. Find the probability
(i) that the number on each die is even.
(ii) that the sum of numbers appearing on the two dice is 5.

• A. i) $\frac{1}{3}$ and ii) $\frac{1}{8}$
• B. i) $\frac{1}{2}$ and ii) $\frac{1}{7}$
• C. i) $\frac{1}{5}$ and ii) $\frac{1}{6}$
• D. i) $\frac{1}{4}$ and ii) $\frac{1}{9}$

Answer 1

Answer: (D)

i) $\frac{1}{4}$ and ii) $\frac{1}{9}$

	$1$	$2$	$3$	$4$	$5$	$6$
$1$	$(1,1)$	$(1,2)$	$(1,3)$	$(1,4)$	$(1,5)$	$(1,6)$
$2$	$(2,1)$	$(2,2)$	$(2,3)$	$(2,4)$	$(2,5)$	$(2,6)$
$3$	$(3,1)$	$(3,2)$	$(3,3)$	$(3,4)$	$(3,5)$	$(3,6)$
$4$	$(4,1)$	$(4,2)$	$(4,3)$	$(4,4)$	$(4,5)$	$(4,6)$
$5$	$(5,1)$	$(5,2)$	$(5,3)$	$(5,4)$	$(5,5)$	$(5,6)$
$6$	$(6,1)$	$(6,2)$	$(6,3)$	$(6,4)$	$(6,5)$	$(6,6)$

(i) Let the event that the number of each die is even.

Favourable outcomes $=\left\{\right(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6\left)\right\}$

Probabaility that number on each dice is even $=\frac{9}{36}=\frac{1}{4}$

(ii) That the sum of numbers appearing on the two dice is $5$.

Favourable outcomes $=\left\{\right(1,4),(2,3),(3,2),(4,1\left)\right\}$

Probability that the sum of the numbers apperaing on the two dice is $5=\frac{4}{36}=\frac{1}{9}$