Statistics Homework Draft, Assignments of Mathematics

1. A couple is planning to have four children.

a. List the sample space of the experiment using tree diagram. There are 16 elements for the

sample space.

S = {GGGG,GGGB, GGBG, GGBB, GBGG, GBGB, GBBG, GBBB, BBBB, BBBG, BBGB, BBGG,

BGBB, BGBG, BGGB, BGGG}

Total: 16

b. What is the probability for the events below?

1) All of the children will be girls: 1/16 = 0.0625 = 6.25%

1234

1 (1,1) (1,2) (1,3) (1,4)

2 (2,1) (2,2) (2,3) (2,4)

3 (3,1) (3,2) (3,3) (3,4)

4 (4,1) (4,2) (4,3) (4,4)

b. What is the probability for the events below?

1) Getting at most one even number: 8/16 = 1/8 = 0.125 = 12.5%

2) Getting at least one even number: 11/16 = 0.6875 = 68.75%

3) That the sum of the numbers is less than 7: 13/16 = 0.8125 = 81.25%

4) That the sum of the numbers is a prime number: 9/16 = 0.5625 = 56.25%