Table of Contents
- 1 What is the probability that only two girls will appear?
- 2 What is the probability that in a family of three children exactly one child will be a girl?
- 3 What are the odds of having 3 of the same gender?
- 4 What are the odds of having 3 boys and 3 girls?
- 5 What are the odds of having a baby in each generation?
- 6 What are the odds of having a child in the nth generation?
What is the probability that only two girls will appear?
It there is a 50\% chance that we will be told the first child is a boy, when there is one of each gender, then the probability of two girls is 50\%.
What is the probability that in a family of three children exactly one child will be a girl?
First, since the chance of a child being a girl is 1/2, the chance of all three being girls is (1/2) (1/2) (1/2) = 1/8. Alternatively, make a list of all possible outcomes, in order of age: {GGG,GGB,GBG,BGG,GBB,BGB,BBG,BBB}. As each one is equally likely, the chance of GGG is again 1/8.
What is the probability of having three girls in a row in one family what is the chance of having a fourth girl in a row?
There is hence a 1 in 2 chance (50\% or 0,5 probability) of either a boy or a girl on each occasion. Therefore, by the multiplication principle, the probability of having 3 girls in a row is 12×12×12=18 . The sex of the 4th child is independent of the sexes of the previous 3 and hence is once again 12 .
What is the probability of getting the same number on both the dice?
1/36
The probability of two dice being the same particular number is 1/6 x 1/6 = 1/36.
What are the odds of having 3 of the same gender?
If you already have a boy, the chance that the next baby is also a boy is 50 percent
| All same sex | Different sexes | |
|---|---|---|
| 2 children | 50\% G/B | 50\% B/G |
| 3 children | 25\% all girl or all boys | 75\% BB/G or GG/B |
| 4 children | 12.5\% all girls or all boys | 37.5\% 1B/3G or 1G/3B |
| 5 children | 6.25\% all boys or all girls | 25\% BBBB/G or GGGG/B |
What are the odds of having 3 boys and 3 girls?
If you already have a boy, the chance that the next baby is also a boy is 50 percent
| All same sex | ||
|---|---|---|
| 3 children | 25\% all girl or all boys | |
| 4 children | 12.5\% all girls or all boys | 50\% BB/GG |
| 5 children | 6.25\% all boys or all girls | 68.75\% GGG/BB or BBB/GG |
| 6 children | 3.125\% all boys or all girls | 46.875\%: GGGG/BB or BBBB/GG |
What is the probability of all three children being girls?
The probability of all three children being girls is the same as that as being all boys, 1 8. And so the probability of the children being all boys or all girls is: P (all boys or all girls) = 1 8 + 1 8 = 1 4
What is the probability of having no boys in each generation?
Conversely the chance of having no boys is 1 / 2 in the first generation, 1 / 4 in the second, and 1 / 8 in the third. This generalizes to 1 / 2 n in the nth generation. (Essentially I’ve drawn a probability tree diagram here, which generalizes to much more complicated problems).
What are the odds of having a baby in each generation?
You can see that the chance of having at least one boy is 1 / 2 in the first generation, 3 / 4 in the second, and 7 / 8 in the third. This generalizes to ( 2 n − 1) / 2 n in the nth generation.
What are the odds of having a child in the nth generation?
You can see that the chance of having at least one boy is 1 / 2 in the first generation, 3 / 4 in the second, and 7 / 8 in the third. This generalizes to ( 2 n − 1) / 2 n in the nth generation. Conversely the chance of having no boys is 1 / 2 in the first generation, 1 / 4 in the second, and 1 / 8 in the third.