In a population of N families, 50% of the families have three children, 30% of…
2004
In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?
- A.
3/23
- B.
6/23
- C.
3/10
- D.
3/5
Attempted by 18 students.
Show answer & explanation
Correct answer: B
Key idea: Weight by number of children. Choose N families, compute total children contributed by each family type, then take the ratio for two-child families.
Three-child families: 50% of N → 0.5N families → children = 0.5N × 3 = 1.5N.
Two-child families: 30% of N → 0.3N families → children = 0.3N × 2 = 0.6N.
One-child families: remaining 20% → 0.2N families → children = 0.2N × 1 = 0.2N.
Total children = 1.5N + 0.6N + 0.2N = 2.3N.
Probability a randomly picked child is from a two-child family = children from two-child families / total children = 0.6N / 2.3N = 0.6 / 2.3 = 6/23.
Answer: 6/23