Question

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.​

Answer 1

• See below

Explanation:

#5

• P(man) = 8/15
• P(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 - 1,4
• 2,1 - 2,2 - 2,3 - 2,4
• 3,1 - 3,2 - 3,3 - 3,4
• 4,1 - 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