OK! Let's rumble -
Most people think this is the same as:
A man has a child, and it's a boy. He then has another child. What is the probability that the second one is a boy too?
The answer to that is 1 in 2, or 50%. It's like saying: if I toss a coin and it comes down heads, what are the odds that it will come down heads next time?
However, this problem is quite different. This is why:
If a man has two children, he could have had:
first a boy, then a girl - BG
first a boy, then another boy - BB
first a girl, then a boy - GB
first a girl, then another girl - GG
These are the only possible ways in which a man can have had 2 children, and they are all equally probable. The probability of each is therefore 1 in 4, or 25%.
Now let's come back to the problem. We know that at least one of the children is a boy. That cuts out just one of the 4 possibilities listed above - GG - leaving 3 possibilities: BG, GB, BB (each of which, as we've seen, is equally likely). Of those 3, only one - BB - satisfies the condition that the other child is a boy as well. So the answer is 1 in 3, or 33.3% (.3 recurring to be precise).
Quite a lot of people refuse to believe this because they think that if a man has two children, he can have two boys, two girls or one of each, ie., three possibilities, each equally likely. But, they're not equally likely, because 'one of each' is not one possibility, but two.
Think of all the people you know with 2 children, and you'll find that roughly a quarter of them have two boys, a quarter have two girls, and half of them have one of each.
What! - What!
Rap:
xxiv) A half a square metre is twice the area of a half metre square.
xxv) 49
Nick (back from vacation, and when I say ?'vacation' read; 'the slammer') agrees.
I am thinking of spending Christmas in Aspen and will be outta here for a while.
May I wish one and all a very happy and safe Christmas.
In the meantime, for anyone who wants to wile away a few minutes:
(Perhaps, Rap or Nick could stand in and confirm any answers)
NOPETS CHRISTMAS QUIZ:
1. The area of a circle 6 meters in diameter exceeds the combined areas of a circle 4 meters in diameter and a circle 2 meters in diameter by how many square meters
2. If @ is defined for all positive numbers a and b by a @ b = 2ab - b2, then
5 @ 2 =
3. Telephone calls cost 20 cents per minute for the first 15 minutes and 10 cents per minute thereafter. Which of the following represents the amount of money needed (in dollars) to talk x minutes (x greater than 15)
$3.00 + $0.10x
$3.00 + $0.10(x-15)
$3.00 + $0.10(15-x)
$3.00 + $0.15x
4. What is the total amount of your purchases if you bought 5 shirts at $m and 2 more shirts at 50% off.
$5m
$6m
$7.5m
$10m
5. If a small cube (side=2) is filled twice and poured into a larger cube (side=4), what will be the height, in inches, of the water in the larger cube
6. Which of the following equations gives the relationship between S and T in the table below
S 1 2 3 4 5 6
T 1 4 7 10 13 16
T = 2 - S
T = 4 - 3S.
T = 3S + 1.
T = 3S - 2.
7. Which of the following proportions is correct if 12 = pq
2:p = 6:q
4:p = 3:q
6:p = 2:q
4:q = p:3
8. A car travels across Texas m miles at the rate of t miles per hour. How many hours does the trip take
9. What is the value of (x + y)(x + y) if xy = -3 and x2 + y2 = 10
10. The vertices of rectangle ABCD are A(-1,0), B(2,0), C(s, t), and D(-1,4). How long is diagonal AC
See ya