Question

Two ordinary six-sided dice were tossed. Set up a sample space for this experiment and

hence find the probability that

i. Sum of the points on the two dice is 7,

ii. Points on the first die are greater than the points on the second die,

iii. First die shows an even number,

Answer 1

Sample Space of the event can be expressed as :

Total Outcomes = 36

i. Sum of the points on the two dice is 7

$$(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\\\text{Total 6 outcomes}$$ $$P(sum=7)=\dfrac{6}{36}=\dfrac{1}{6}$$

ii. Points on the first die are greater than the points on the second die

$$(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3), (5,1), (5, 2),$$ $$(5, 3), (5, 4),(6,1), (6, 2), (6, 3), (6, 4), (6, 5)\\\text{Total 15 outcomes}$$ $$P(first\ is\ greater)=\dfrac{15}{36}=\dfrac{5}{12}$$

iii. First die shows an even number

$$(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),$$ $$(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),$$ $$6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\\\text{Total 18 outcomes}$$ $$P(first\ is\ even)=\dfrac{18}{36}=\dfrac{1}{2}$$