For me both problem 2 and problem 3 should also be 1/2 .
The variances are due to how people interpret the outcome space .
It is right that probability = favaroble out comes / total possible outcomes.
In problem 2, in my opinion the possible outcomes are not how it was suggested in the post but as below. When a family has 2 kids , the below are the only possible outcomes
1) Potential Outcome 1: Both are boys
2) Potential Outcome 2: One boy and one girl
3) Potential outcome 3: Both are girls
The 3rd one is not a legal potential outcome in our particular constraint of problem 2, since problem #2 statement already states 'at least one is a boy'
So Total possible legal outcomes = 2
Favorable out comes for our event (both boys) = 1
So probability for Problem 2 = 1/2
Similarly for problem #3, I think the post unnecessarily complicates the calculation of problem space. The fact that 'Tuesday' is mentioned is irrelevant in my opinon, if you state the problem #3 in a different way that is more clearly understood.
There are 14 baskets labelled as follows "Sunday Boy", "Sunday Girl", "Monday Boy", "Monday Girl",....."Saturday Boy", "Saturday Girl". A stork came and dropped 2 babies. One baby was dropped in "Tuesday Boy" basket. What is the probability that both are boys?
Now the total outcomes and favarable outcomes are :
Total possible outcomes = Number of ways second baby could have been dropped = 14 possible baskets = 14
Favorable outcomes = second baby dropped in 'boy' basket = 7 possible baskets = 7
Probability that both are boys = 7 / 14 = 1/2
The variances are due to how people interpret the outcome space .
It is right that probability = favaroble out comes / total possible outcomes.
In problem 2, in my opinion the possible outcomes are not how it was suggested in the post but as below. When a family has 2 kids , the below are the only possible outcomes
1) Potential Outcome 1: Both are boys 2) Potential Outcome 2: One boy and one girl 3) Potential outcome 3: Both are girls
The 3rd one is not a legal potential outcome in our particular constraint of problem 2, since problem #2 statement already states 'at least one is a boy'
So Total possible legal outcomes = 2 Favorable out comes for our event (both boys) = 1
So probability for Problem 2 = 1/2
Similarly for problem #3, I think the post unnecessarily complicates the calculation of problem space. The fact that 'Tuesday' is mentioned is irrelevant in my opinon, if you state the problem #3 in a different way that is more clearly understood.
There are 14 baskets labelled as follows "Sunday Boy", "Sunday Girl", "Monday Boy", "Monday Girl",....."Saturday Boy", "Saturday Girl". A stork came and dropped 2 babies. One baby was dropped in "Tuesday Boy" basket. What is the probability that both are boys?
Now the total outcomes and favarable outcomes are :
Total possible outcomes = Number of ways second baby could have been dropped = 14 possible baskets = 14
Favorable outcomes = second baby dropped in 'boy' basket = 7 possible baskets = 7
Probability that both are boys = 7 / 14 = 1/2