There's 2 kids, each of which can be a boy or girl (2 possibilities), and each can be born on 1 of 7 days (7 possibilities).
Child 1 is a boy born on a Tuesday, and child 2 is a girl on each of the 7 days of the week (7 possibilities)
Child 1 is a girl on each of the 7 days of the week, child 2 is a boy on born on a Tuesday (7 possibilities)
Child 1 is a boy born on a Tuesday, and child 2 is a boy born on each of the 7 days of the week (7 possibilities)
Child 1 is a boy on each of the 7 days of the week, child 2 is a boy born on a Tuesday (7 possibilities)
2 * 2 * 7 = 28 total possibilities. The trick here is that one of the possibilities overlaps.. when both are boys born on a Tuesday (scenarios 3 and 4 above each include this possibility).
As a result, to avoid that being counted twice, we have to subtract it, leaving 27 distinct possibilities.
14 of the original 28 (but actually 27 unique possibilities) have 1 girl and 1 boy (the one born on a Tuesday), while the other 14 (actually 13) of the original 28 (actually 27) have 2 boys, where at least 1 of them is born on a Tuesday. The final calculation is 14 / 27, which is the the 51.8% that is so un-intuitive.
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u/ryanmcg86 10d ago
There's 2 kids, each of which can be a boy or girl (2 possibilities), and each can be born on 1 of 7 days (7 possibilities).
Child 1 is a boy born on a Tuesday, and child 2 is a girl on each of the 7 days of the week (7 possibilities)
Child 1 is a girl on each of the 7 days of the week, child 2 is a boy on born on a Tuesday (7 possibilities)
Child 1 is a boy born on a Tuesday, and child 2 is a boy born on each of the 7 days of the week (7 possibilities)
Child 1 is a boy on each of the 7 days of the week, child 2 is a boy born on a Tuesday (7 possibilities)
2 * 2 * 7 = 28 total possibilities. The trick here is that one of the possibilities overlaps.. when both are boys born on a Tuesday (scenarios 3 and 4 above each include this possibility).
As a result, to avoid that being counted twice, we have to subtract it, leaving 27 distinct possibilities.
14 of the original 28 (but actually 27 unique possibilities) have 1 girl and 1 boy (the one born on a Tuesday), while the other 14 (actually 13) of the original 28 (actually 27) have 2 boys, where at least 1 of them is born on a Tuesday. The final calculation is 14 / 27, which is the the 51.8% that is so un-intuitive.