WEBVTT
1
00:00:01.590 --> 00:00:04.540 A:middle L:90%
all right, we're given some statistics about a company
2
00:00:04.540 --> 00:00:09.070 A:middle L:90%
that offers its clients insurance. 70% of those with
3
00:00:09.080 --> 00:00:11.699 A:middle L:90%
Onley Life insurance renew their plan for the next year
4
00:00:12.070 --> 00:00:14.529 A:middle L:90%
. 80% of those with only medical insurance renew their
5
00:00:14.529 --> 00:00:17.519 A:middle L:90%
plans for next year and 90% with both renew their
6
00:00:17.519 --> 00:00:20.210 A:middle L:90%
plans for next year. In addition, 75% of
7
00:00:20.210 --> 00:00:23.670 A:middle L:90%
these clients have life insurance, 45% of medical insurance
8
00:00:24.239 --> 00:00:27.170 A:middle L:90%
and 20% have both. So to start, I'm
9
00:00:27.170 --> 00:00:32.049 A:middle L:90%
gonna note probability that a given client on Lee has
10
00:00:32.049 --> 00:00:37.140 A:middle L:90%
life insurance, and that's simply the probability that they
11
00:00:37.140 --> 00:00:40.490 A:middle L:90%
have life insurance, minus the probability they have both
12
00:00:40.490 --> 00:00:47.679 A:middle L:90%
. So that's gonna be 0.75 0.20 point 55 Do
13
00:00:47.679 --> 00:00:49.590 A:middle L:90%
the same. With the probability of only having medical
14
00:00:49.590 --> 00:00:54.859 A:middle L:90%
insurance, she's gonna be the probability of having medical
15
00:00:54.859 --> 00:00:58.619 A:middle L:90%
insurance in general, which is 0.45 minus the probability
16
00:00:58.619 --> 00:01:03.129 A:middle L:90%
of having both 0.20 point 25 all right. For
17
00:01:03.129 --> 00:01:07.049 A:middle L:90%
the first part, we want to know the probability
18
00:01:08.239 --> 00:01:11.120 A:middle L:90%
that a given client renews at least one of their
19
00:01:11.120 --> 00:01:12.750 A:middle L:90%
policies for the next year, and we're going to
20
00:01:12.750 --> 00:01:15.420 A:middle L:90%
use a lot of total probability for that. So
21
00:01:15.420 --> 00:01:17.920 A:middle L:90%
that's gonna be the probability of having only life insurance
22
00:01:19.140 --> 00:01:23.680 A:middle L:90%
times the probability that a client renews, given that
23
00:01:23.680 --> 00:01:27.060 A:middle L:90%
they have Onley life insurance, Onley There we go
24
00:01:30.519 --> 00:01:34.480 A:middle L:90%
. Plus the probability of only having medical insurance times
25
00:01:34.480 --> 00:01:38.120 A:middle L:90%
the probability that they were new, given they only
26
00:01:38.120 --> 00:01:44.950 A:middle L:90%
have medical insurance, plus the probability that they have
27
00:01:44.950 --> 00:01:49.620 A:middle L:90%
both times the probability they renew, given that they
28
00:01:49.620 --> 00:01:55.340 A:middle L:90%
have both. All right, if we plug everything
29
00:01:55.340 --> 00:02:04.093 A:middle L:90%
in, we get 0.55 times zero 0.7 plus 0.25
30
00:02:04.533 --> 00:02:15.902 A:middle L:90%
time 0.8 waas zero point What's the 0.2? I'm
31
00:02:15.902 --> 00:02:20.103 A:middle L:90%
0.9. If we write this out, that gives
32
00:02:20.103 --> 00:02:27.182 A:middle L:90%
us 0.765 All right party. We want to find
33
00:02:27.182 --> 00:02:30.742 A:middle L:90%
the probability that somebody that given that they were new
34
00:02:31.133 --> 00:02:35.242 A:middle L:90%
, their policy next year the probability they have both
35
00:02:35.242 --> 00:02:39.223 A:middle L:90%
kinds of insurance, So ability of both given that
36
00:02:39.223 --> 00:02:43.163 A:middle L:90%
they were new for that, we're just going to
37
00:02:43.163 --> 00:02:45.342 A:middle L:90%
use based room. So that's gonna be the probability
38
00:02:45.712 --> 00:02:53.453 A:middle L:90%
that they have both times the probability that they renew
39
00:02:53.453 --> 00:03:00.652 A:middle L:90%
given they have both over probability. But they were
40
00:03:00.652 --> 00:03:05.073 A:middle L:90%
new, all right, so the probability they have
41
00:03:05.073 --> 00:03:08.853 A:middle L:90%
both 0.2 The probability they renew, given they have
42
00:03:08.853 --> 00:03:13.073 A:middle L:90%
both 0.9 On the last part, We computed that
43
00:03:13.073 --> 00:03:16.353 A:middle L:90%
the probability that they were new is 0.765 If you
44
00:03:16.353 --> 00:03:23.032 A:middle L:90%
compute this out, that is 0.25 Sorry, it's
45
00:03:23.032 --> 00:03:30.842 A:middle L:90%
not 0.250 point 235 three and there you have it
46
--> A:middle L:90%
.