Answer:
The probability of randomly meeting a four child family with either exactly one or exactly two boy children = (5/8) = 0.625
Step-by-step explanation:
Complete Question
The probability of randomly meeting a four child family with either exactly one or exactly two boy children.
Solution
The possible sample spaces for a family with four children include
4 boys and 0 Girl
BBBB
3 boys and 1 girl
BBBG BBGB BGBB GBBB
2 boys and 2 girls
BBGG BGBG BGGB GBBG GBGB GGBB
1 boy and 3 girls
BGGG GBGG GGBG GGGB
0 boy and 4 girls
GGGG
Total number of elements in the sample space = 16
Probability of an event is defined as the number of elements in that event divided by the Total number of elements in the sample space.
The required probability is a sum of probabilities.
The probability of meeting a four child family with exactly 1 boy = (4/16) = (1/4) = 0.25
The probability of meeting a four child family with exactly 2 boys = (6/16) = (3/8) = 0.375
The probability of randomly meeting a four child family with either exactly one or exactly two boy children = (4/16) + (6/16) = (10/16) = (5/8) = 0.25 + 0.375 = 0.625
Hope this Helps!!!
