See image for question. Question Continuation :
1.construct a table for the sample space of the random experiment.
2.using the sample space find the probability that the total score of the two dice is:
a. greater than or equal to 5
b. greater than 5 but less than 8.​

See below

Step-by-step explanation:

#5

P(man) = 8/15P(lady) = 7/15

(a)

P(both ladies) = 7/15*6/14 = 1/5

(b)

P(both men) = 8/15*7/14 = 4/15

(c)

P(same sex) = P(both men or both ladies) = 1/5 + 4/15 = 7/15

(d)

P(different sexes) = P(man and lady or lady and man) = 8/15*7/14 + 7/15*8/14 = 8/15

Another way:

P(different sexes) = 1 - P(both ladies) - P(both men) = 1 - 1/5 - 4/15 = 8/15

#6

Sample space:

1, 1 - 1,2 - 1,3 - 1,42,1 - 2,2 - 2,3 - 2,43,1 - 3,2 - 3,3 - 3,44,1 - 4,2 - 4,3 - 4,4

Total 16 outcomes

a)

P(sum ≥5) = 10/16 = 5/8

b)

P(5<sum<8) = P(6 or 7) = 5/16

It is the top one. the answer is -7. that is smallest