30. TWO QUESTIONS IN PROBABILITIES. There is perhaps no class of puzzle over which people so frequently blunder as that which involves what is called the theory of probabilities. I will give two simple examples of the sort of puzzle I mean. They are really quite easy, and yet many persons are tripped up by them. A friend recently produced five pennies and said to me: "In throwing these five pennies at the same time, what are the chances that (1/2)

SOLUTION TO 30. TWO QUESTIONS IN PROBABILITIES. (1/4) 

In tossing with the five pennies all at the same time, it is obvious that there are 32 different ways in which the coins may fall, because the first coin may fall in either of two ways, then the second coin may also fall in either of two ways, and so on. Therefore five 2's multiplied together make 32. Now, how are these 32 ways made up? Here they are:--

(a) 5 heads 1 way
(b) 5 tails 1 way

Show thread

SOLUTION TO 30. TWO QUESTIONS IN PROBABILITIES. (2/4) 

...
(c) 4 heads and 1 tail 5 ways
(d) 4 tails and 1 head 5 ways
(e) 3 heads and 2 tails 10 ways
(f) 3 tails and 2 heads 10 ways

Now, it will be seen that the only favourable cases are a, b, c,
and d--12 cases. The remaining 20 cases are unfavourable, because they do not give at least four heads or four tails. Therefore the chances are

Show thread
Follow

SOLUTION TO 30. TWO QUESTIONS IN PROBABILITIES. (3/4) 

...
only 12 to 20 in your favour, or (which is the same thing) 3 to 5. Put another way, you have only 3 chances out of 8.

The amount that should be paid for a draw from the bag that contains three sovereigns and one shilling is 15s. 3d. Many persons will say that, as one's chances of drawing a sovereign were 3 out of 4, one should pay three-fourths of a pound, or 15s., overlooking the fact that

· tooter · 1 · 0 · 0

SOLUTION TO 30. TWO QUESTIONS IN PROBABILITIES. (4/4) 

...
one must draw at least a shilling--there being no blanks.

Show thread
Sign in to participate in the conversation
Mathstodon

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!