# simple probability question - don't understandWatch

#1
The question is as follows:

Hen pigeons occur with probability (1/2).
I place three pigeons in a box. What is the chance of a mating pair?

To solve this, I drew a tree diagram and ended up with six different possibilities, ie. 6 x (1/2) x (1/2) x (1/2) = 6 x (1/8) = 3/4

I get that.

BUT, it then says:
How many pigeons must I place in a box to be 99% sure of at least one mating pair?

And I just don't understand what I should do to find this out! Please could someone help?
0
7 years ago
#2
(Original post by sophgen)
The question is as follows:

Hen pigeons occur with probability (1/2).
I place three pigeons in a box. What is the chance of a mating pair?

To solve this, I drew a tree diagram and ended up with six different possibilities, ie. 6 x (1/2) x (1/2) x (1/2) = 6 x (1/8) = 3/4

I get that.

BUT, it then says:
How many pigeons must I place in a box to be 99% sure of at least one mating pair?

And I just don't understand what I should do to find this out! Please could someone help?
You need to turn the question around. Rather than 99% of at least one mating pair, you want to consider less than 1% of no mating pairs.

So, say you have n pigeons, what't the probability that you don't have a mating pair, i.e. they are all the same sex; and this will be a function of n, that needs to be less than 0.01
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