00:01
In this scenario, we have 20 bridge pairs, seated 1 through 20, that are randomly divided into 10 east -west pairs and 10 north -south pairs.
00:13
And for part a, we are interested in the number of top -10 pairs that end up playing in the east -west direction.
00:22
So from the question, we have 20 pairs of players.
00:30
And for the top 10 pairs, that group is of size 10.
00:39
And we're interested in how many end up playing in one of the two divisions, the east -west division.
00:45
So that sample size is 10.
00:48
That's half of the population are in the east -west and half are in the north -south.
00:57
And so for part a we are asked, what is the probability that x of the top 10 pairs end up playing east -to -west? so this is the probability mass function for a hyper -geometric random variable.
01:12
And it has the following formula.
01:14
And if we plug in these numbers, we have 10 choose x times 10 choose 10 minus x divided by 20 choose 10.
01:55
And this is for x being an integer between 0 and 10.
02:16
And next for part b, we are asked the probability that all of the top five pairs end up playing the same direction.
02:23
So now, rather than being interested in the group of people that are the top 10 pairs, we are interested in the top 5 pairs.
02:31
So now m is a group of size 5, and everything else stays the same.
02:37
So we still have a population of 20.
02:39
We still have 10 in each direction division.
02:43
Our random variable x now is the number of top 5 pairs that end up playing in the east -west division.
02:51
So the probability that all top five pairs play in the same division is the probability that five of them play in the east -west or none of them play in the east -west, in which case all of them are in the north -south...