Suppose that a family wants to have four children. (Enter the probabilities as f

Question

Suppose that a family wants to have four children. (Enter the probabilities as fractions.)
a) what is the sample space? (Let B represent a boy and G represent a girl. To indicate that the first child is a boy, the second child is a boy, the third child is a boy, and the fourth child is a girl enter BBBG. Enter your answers as a comma-separated list.)
b) what is the probability of 4 girls?
c) what is the probability of 4 boys? what is the probability of 1 boy and 3 girls?
d) what is the probability of 2 boys and 2 girls?
e) what is the sum of your answers in parts (b) - (d)? (a) what is the sample space? (uet 8 represent a boy and G reperesene a girt. to indicate that the fiest hils is a bay the second chila is a boy the third child is a boy, and t Yourth childis agit r nter our nsers as a condis What is the probabilty of 2 brys and 2 gih

Explanation / Answer

a) Sample space or all the possibilities would be BBBB. BBBG, BBGB, BGBB, GBBB, BBGG, BGBG, BGGB, GBGB, GGBB, GBBG, BGGG, GBGG, GGBG, GGGB, GGGG.

b) Probability of 4 girls = No. of ways of having 4 girls/ Total No. of ways = 1/16

c) Probability of 4 boys = Probability of 4 girls = 1/16
Probability of 1 boy and 3 girls = 4/16 = 1/4

d) Probability of 2 boys and 2 girls = 6/16 = 3/8

e) Sum of answers from (b) to (d) = 1/16 + 1/16 + 1/4 + 3/8 = 1/2

  

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