Question

Two Dice are thrown at the same time (a) How many sample points are there for the outcome? (b) What is the probability that the sum of the numbers is a total of 9? (c) What is the probability that at least one of the dice outcome is a 6? (d) What is the probability that the sum of the numbers is a total of 12? (e) Draw a venn diagram for events A, B and C? (f) Find P(AnB) (g) Find P(AUB)

need help with Statistics assignment

Answer 1

a)When two dice are thrown simultaneously, then  number of sample points are 6²= 36 because each die has 1 to 6 number on its faces.The sample points are :

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

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

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

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

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

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

b) Let A be the event that sum is 9. Possible outcomes are (3,6),(4,5),(5,4),(6,3) i.e 4 possible outcomes ,thus

P(A)=4/36=0.111111

c) Let B be the event that at least one of the dice outcome is 6.Possible outcomes are (1,6),(2,6),(3,6),(4,6),(5,6),(6,6),(6,1),(6,2),(6,3),(6,4),(6,5)

so P(B)= 11/36= 0.305555

d)Let C be the event that sum is 12.There is only one possible outcome (6,6) so

P(C)=1/36= 0.027777

f) P(A int B)=P( sum is 9 and at least one of the dice outcome is 6)

common outcome is (3,6) only .Therefore, P(A int B)= 1/36= 0.027777

g) P(A union B)=P(sum is 9 or at least one of the dice outcome is 6)

possible outcomes are :(1,6),(2,6),(3,6),(4,6),(5,6),(6,6),(6,1),(6,2),(6,3),(6,4),(6,5),(4,5),(5,4),(6,3).

P(A union B)= 14/36= 0.388888