Difference between revisions of "2014 AMC 8 Problems/Problem 18"
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Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely? | Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely? | ||
| − | (A) | + | <math>\textbf{(A) }</math> All are boys <math>\qquad\textbf{(B) }</math> All are girls <math>\qquad\textbf{(C) }</math> 2 are boys and 2 are girls <math>\qquad\textbf{(D) }</math> 3 are the same gender and 1 is not <math>\qquad \textbf{(E) }</math> They all have the same probability of happening |
| − | (B) | ||
| − | (C) 2 are | ||
| − | (D) 3 are | ||
| − | (E) all of | ||
==Solution 1== | ==Solution 1== | ||
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| − | So out of the four fractions, D is the largest. So our answer is <math>\boxed{\text{(D) | + | So out of the four fractions, D is the largest. So our answer is <math>\boxed{\text{(D) 3 are of one gender and 1 is of the other gender}}.</math> |
==Video Solution (CREATIVE THINKING)== | ==Video Solution (CREATIVE THINKING)== | ||
Latest revision as of 22:36, 11 August 2025
Problem
Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely?
All are boys 
All are girls 
2 are boys and 2 are girls 
3 are the same gender and 1 is not 
They all have the same probability of happening
Solution 1
We'll just start by breaking cases down. The probability of A occurring is 
. The probability of B occurring is .
The probability of C occurring is 
, because we need to choose 2 of the 4 slots to be girls.
For D, there are two possible cases, 3 girls and 1 boy or 3 boys and 1 girl. The probability of the first case is 
because we need to choose 1 of the 4 slots to be a boy. However, the second case has the same probability because we are choosing 1 of the 4 children to be a girl, so the total probability is 
.
So out of the four fractions, D is the largest. So our answer is 
Video Solution (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
https://youtu.be/3bF8BAvg0uY ~savannahsolver
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 17 |
Followed by Problem 19 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
