# Two dice are rolled and the sum is calculated. Find: a) the probability of a sum of 5. _____ b) the odds for a sum of seven. _____ c) the…

A. What were the odds against Jet winning a race? _____

b) What were the odds against Fleet winning a race? _____

c) What was the probability of Jet winning a race? _____

d) What was the probability of Fleet winning a race? _____

8. Two cards are drawn without replacement from an ordinary deck. Find the probability that

a) the second is a 7 given the first is also a 7. _____

b) the second is a queen given the first is not a queen. _____

c) two spades are drawn. _____

9.  Two-thirds of the population are on a diet at least occasionally. Of this group, 4/5 drink diet soft drinks, while 1/2 of the rest of the population drink diet soft drinks. Complete A tree below (labels AND probabilities) and then answer the questions below.

Let D = those who diet, then D’ = _________________________ (in words)

Let S = those who drink diet soft drinks, then S’ = ________________________ (in words)

10. Draw and Shade Venn Diagrams below to represent the set given

A. A∪B′

B. (A∪B′)∪C

C. (A∪B′)∪C′

D. (A∪B′)∩C

E. (A∪B′)∩C′

F. A∩B′

G. (A∩B′)∪C

H. (A∩B′)∪C′

I. (A∩B′)∩C

J. (A∩B′)∩C′

Solutiona) Number of ways to make a sum of 5 = (1,4), (2,3), (3,2), (4,1)So, probability of a sum of 5 = 4/36 = 1/9b) Number of ways to make a sum of 7 = (1,6), (2,5), (3,4), (4,3), (5,2),… 