Source : https://www.hackerrank.com/challenges/s10-mcq-4
Objective
In this challenge, we get started with conditional probability. Check out the Tutorial tab for learning materials!
Task
Suppose a family has children, one of which is a boy. What is the probability that both children are boys?
Source : https://www.hackerrank.com/challenges/s10-mcq-4
Solution
| github.com/RodneyShag | |
| Answer: 1/3 | |
| ****** 2 valid answers: 1/3 or 1/2 | |
| Reference: https://en.wikipedia.org/wiki/Boy_or_Girl_paradox | |
| This question is known as the "Boy or Girl Paradox". The actual answer is either 1/3 or 1/2 | |
| depending on how the question is interpreted. Here are 2 ways to interpret the question: | |
| 1) From all families with two children, at least one of whom is a boy, a family is | |
| chosen at random. This would yield the answer of 1/3. | |
| 2) From all families with two children, one child is selected at random, and the sex | |
| of that child is specified to be a boy. This would yield an answer of 1/2. | |
| ******* Interpretation (1) gives an answer of 1/3 | |
| There are 4 possible scenarios: (B, B), (B, G), (G, B), (G, G) | |
| We know that 1 child is a boy, so now we have 3 scenarios: (B, B), (B, G), (G, B) | |
| When asked, "what is the probability that both children are boys", the only scenario that | |
| matches this is: (B, B). That is, only 1 of the 3 scenarios satisfies the critera, so | |
| there is a 1/3 chance that both children are boys. | |
| ******* Interpretation (2) gives an answer of 1/2 | |
| In this scenario, a child was selected at random from a set of all children that have | |
| exactly 1 sibling. Knowing the fact that the child is a boy does not give us any | |
| information on whether his sibling is a boy or a girl. | |
| ******* HackerRank's correct answer | |
| The accepted answer on HackerRank is 1/3. This aligns with the fact | |
| that the problem wording more closely resembles Interpretation (1). |
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