WEBVTT
1
00:00:01.740 --> 00:00:07.240 A:middle L:90%
Now we have 54 Republicans, two independent and 44
2
00:00:07.240 --> 00:00:13.310 A:middle L:90%
Democrats in the Senate. And suppose we randomly select
3
00:00:13.320 --> 00:00:19.059 A:middle L:90%
three senators. Two form a new community. We
4
00:00:19.059 --> 00:00:23.140 A:middle L:90%
want to know the probable probability for the following three
5
00:00:23.140 --> 00:00:29.940 A:middle L:90%
situations. And first, let's, um, compute
6
00:00:29.949 --> 00:00:33.869 A:middle L:90%
the total number of people in the Senate. It
7
00:00:33.869 --> 00:00:50.689 A:middle L:90%
is 54 plus two plus 44 and those equals 100
8
00:00:53.539 --> 00:01:00.359 A:middle L:90%
. And then oops. Let's look at Part eight
9
00:01:00.740 --> 00:01:07.349 A:middle L:90%
, where all three senators come from Republicans. Um
10
00:01:11.939 --> 00:01:23.680 A:middle L:90%
, so probability of three Republicans. And this is
11
00:01:23.680 --> 00:01:32.540 A:middle L:90%
easy because we wanna choose three out of 54 Republicans
12
00:01:32.620 --> 00:01:38.829 A:middle L:90%
divided by the the number, the total number of
13
00:01:38.829 --> 00:01:44.530 A:middle L:90%
choices of choosing three senators. So this should be
14
00:01:44.530 --> 00:01:53.120 A:middle L:90%
100. Choose three. And this equals these air
15
00:01:53.120 --> 00:01:57.439 A:middle L:90%
. Quite large numbers. So we have to use
16
00:01:57.439 --> 00:02:10.050 A:middle L:90%
calculator for this. Finally, the probability is 0.153
17
00:02:12.139 --> 00:02:16.389 A:middle L:90%
Okay, Next we want to know the probability of
18
00:02:16.400 --> 00:02:29.139 A:middle L:90%
all three senators comes come from Democrats, and this
19
00:02:29.139 --> 00:02:31.689 A:middle L:90%
is similar to part eight, and we want to
20
00:02:31.689 --> 00:02:39.340 A:middle L:90%
choose three out of 44 Democrats divided by the total
21
00:02:39.340 --> 00:02:52.650 A:middle L:90%
number of choices, which is 100 shoes three and
22
00:02:52.650 --> 00:02:57.610 A:middle L:90%
we can recycle the value of the denominator from part
23
00:02:57.610 --> 00:03:10.250 A:middle L:90%
A. And this equals 2.0, 82. And
24
00:03:12.979 --> 00:03:15.659 A:middle L:90%
now, part C is a little bit different because
25
00:03:15.659 --> 00:03:22.009 A:middle L:90%
we wanted select one from each party. So this
26
00:03:22.009 --> 00:03:30.569 A:middle L:90%
is actually 33 steps, So one from each.
27
00:03:37.039 --> 00:03:42.169 A:middle L:90%
Now we wanna first select one from the Republicans.
28
00:03:42.639 --> 00:03:51.229 A:middle L:90%
This is 54. Choose one times, select one
29
00:03:51.229 --> 00:03:54.360 A:middle L:90%
from independent. This is to choose one times.
30
00:03:55.939 --> 00:04:01.909 A:middle L:90%
Um, so that one from Democrats for a fortunes
31
00:04:01.909 --> 00:04:10.039 A:middle L:90%
one divided by Sorry. Ah, 100 shoes.
32
00:04:10.110 --> 00:04:30.000 A:middle L:90%
Three The Sequels 54 times, two times 44 divided
33
00:04:30.000 --> 00:04:42.970 A:middle L:90%
by the same denominator. And those equals 0.29 and
34
00:04:42.970 --> 00:04:43.670 A:middle L:90%
we're done.