Question

Out of 2000 families with four Children each,

Answer 1

Answer:

Two boys

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

based on the rough assumption that the probabilty to get a boy is the same as to get a girl = 1/2 = 0.5, as there are only 2 possible outcomes.

when a family has 4 children, they have 2 possibilities for the first child, 2 for the second child, 2 for the third and 2 for the fourth child.

so, 2×2×2×2 = 2⁴ = 16 possibilities.

the probability for any of these 16 possibilities is

0.5⁴ = (1/2)⁴ = 1/16 = 0.0625

how many of these 16 possibilities include at least one boy ? all except the one, where all 4 children are girls.

so, 16 - 1 = 15

that means 15 out of possible 16 different "configurations" contain at least 1 boy.

the probabilty is therefore 15/16.

and that applies as mean value of 2000 families to

2000 × 15/16 = 125 × 15 = 1875 families

we expect 1875 families out of 2000 to have at least one boy.

how many have 2 boys ?

that is the same as the question in how many ways can I pick 2 elements out of 4.

that are 4 over 2 combinations

4! / (2! × (4-2)!) = 4!/(2!×2!) = 4×3/2 = 2×3 = 6

so, 6 out of the possible 16 possibilities have 2 boys.

the probabilty is therefore 6/16 = 3/8

and that applies as mean value of 2000 families to

2000 × 6/16 = 125 × 6 = 750 families

we expect 750 families out of 2000 to have two boys.

how many have 1 or 2 girls ?

there are 4 possibilities to have 1 girl (either the first, the second, the third or the fourth child).

there are (as before with the 2 boys) 6 possibilities to have 2 girls.

that is together 4+6=10 possibilities out of the 16 to have one or two girls.

the probabilty is therefore 10/16 = 5/8

and that applies as mean value of 2000 families to

2000 × 10/16 = 125 × 10 = 1250 families

we expect 1250 families out of 2000 to have one or two girls.

how many have no girls ?

that is the same as having only (4) boys.

there is only one possibility out of the 16 for that.

the probabilty is therefore 1/16.

and that applies as mean value of 2000 families to

2000 × 1/16 = 125 families

we expect 125 families out of 2000 to have no girls.