WEBVTT 00:00:00.637 --> 00:00:02.970 Lad os lave lidt sandsynlighedsregning med kort. 00:00:02.970 --> 00:00:04.511 I denne video vil vi antage 00:00:04.511 --> 00:00:06.864 at der ingen jokere er. 00:00:06.864 --> 00:00:08.780 Du kan lave samme opgaver med en joker, 00:00:08.780 --> 00:00:11.560 men så er tallene blot lidt anderledes. 00:00:11.560 --> 00:00:13.390 Med det sagt, 00:00:13.390 --> 00:00:15.800 lad os først huske hvor mange kort, 00:00:15.800 --> 00:00:18.210 der er i et sæt spillekort. 00:00:18.210 --> 00:00:23.040 Du har 4 kulører, spar, ruder 00:00:23.040 --> 00:00:26.960 klør og hjerter. 00:00:26.960 --> 00:00:29.770 Du har 4 kulører og i hver af dem 00:00:29.770 --> 00:00:31.950 er der 13 forskellige kort 00:00:31.950 --> 00:00:33.640 eller 00:00:43.970 --> 00:00:47.920 Du har esset, så har du en 2'er, en 3'er, en 4'er 00:00:47.920 --> 00:00:52.210 en 5'er, en 6'er, 7, 8, 9, 10 00:00:52.210 --> 00:00:55.620 og så har du knægt, konge og dame. 00:00:55.620 --> 00:00:57.590 Det er i alt 13 kort. 00:00:57.590 --> 00:01:00.890 For hver kulør har du hver af disse. 00:01:00.890 --> 00:01:03.480 D 00:01:03.480 --> 00:01:05.910 Du kan have en ruder knægt, en klør knægt 00:01:05.910 --> 00:01:09.220 en spar knægt eller en hjert knægt. 00:01:09.220 --> 00:01:10.970 Når du ganger disse, 00:01:10.970 --> 00:01:13.532 Du tager et sæt spillekort og fjerner jokerne, 00:01:13.532 --> 00:01:15.240 og tælle dem, men du kan ogå 00:01:15.240 --> 00:01:18.740 gange de 4 kulører, hver med 13 kort. 00:01:18.740 --> 00:01:21.120 Du har 4 gange 13, som er 52 kort et sæt.s 00:01:21.120 --> 00:01:24.207 s 00:01:24.207 --> 00:01:25.790 Eller du kan sige, 00:01:25.790 --> 00:01:28.270 der er 13 af hver kulør 00:01:28.270 --> 00:01:31.120 og der er 4 kulører 00:01:31.120 --> 00:01:33.237 så igen 13 gange 4 og du får 52 kort. 00:01:33.237 --> 00:01:34.820 Lad os se på sandsynligheden for 00:01:34.820 --> 00:01:37.156 forskellige hændelser. 00:01:37.156 --> 00:01:38.530 Lad os sige jeg blander kortene godt. 00:01:38.530 --> 00:01:40.610 Jeg blander dem rigtig godt 00:01:40.610 --> 00:01:43.240 og så vælger jeg tilfældigt et kort fra bunken. 00:01:43.240 --> 00:01:46.400 Hvad er sandsynligheden for at 00:01:46.400 --> 00:01:50.220 jeg trækker en knægt? 00:01:50.220 --> 00:01:53.450 Hvor mange lige sandsynlige hændelser er der? 00:01:53.450 --> 00:01:56.540 Du kan vælge ethvert af de 52 kort. 00:01:56.540 --> 00:02:00.350 Der er 52 muligheder for at trække et kort. 00:02:00.350 --> 00:02:04.130 Hvor mange af de 52 muligheder er knægte? 00:02:04.130 --> 00:02:07.480 Du har spar knægt, ruder knægt, 00:02:07.480 --> 00:02:09.880 kør knægt og hjerter knægt. 00:02:09.880 --> 00:02:14.170 Der er 4 knægte i et sæt. 00:02:14.170 --> 00:02:18.090 Det er 4/52. Disse kan begge dividiers med 4 00:02:18.090 --> 00:02:23.060 4 divideret med 4 er 1. 52 divideret med 4 er 13. 00:02:23.060 --> 00:02:27.390 Hvad er sandsynligheden. 00:02:27.390 --> 00:02:28.976 Jeg gør det lige igen. 00:02:28.976 --> 00:02:30.600 Jeg putter knægten tilbage. 00:02:30.600 --> 00:02:31.850 blander kortene igen. 00:02:31.850 --> 00:02:34.020 Så jeg igen har 52 kot. 00:02:34.020 --> 00:02:37.290 Hvad er sandsynligheden for at få en hjerter+ 00:02:37.290 --> 00:02:39.290 Hvad er sandsynligheden for at jeg tilfældgit 00:02:39.290 --> 00:02:43.720 fra et blandet sæt trækker en hjerter? 00:02:43.720 --> 00:02:46.580 Der er igen 52 mulige kort. 00:02:46.580 --> 00:02:47.480 jeg kan vælge i mellem. 00:02:47.480 --> 00:02:51.720 52 lige sandsynlige muligheder. 00:02:51.720 --> 00:02:55.010 Hvor mange af dem er hjerter? 00:02:55.010 --> 00:02:57.770 13 af dem er hjertere. 00:02:57.770 --> 00:03:00.180 Der er 13 kort i hver kulør. 00:03:00.180 --> 00:03:01.892 så der er 13 hjertere i sættet. 00:03:01.892 --> 00:03:03.350 Der er 13 rudere i sættet. 00:03:03.350 --> 00:03:04.970 Der er 13 sparer i sættet. 00:03:04.970 --> 00:03:07.490 Der er 13 klører i sættet 00:03:07.490 --> 00:03:12.570 13 ud af 52 vil være en hjerter, og begge disse 00:03:12.570 --> 00:03:14.270 kan divideres med 13. 00:03:14.270 --> 00:03:16.670 Det er det samme som 1/4. 00:03:16.670 --> 00:03:19.040 1 ud af 4 gange vil jeg få en hjerter 00:03:19.040 --> 00:03:21.690 eller jeg har en sandsynlighed på 1 ud af for at få en hjerter. 00:03:21.690 --> 00:03:24.619 når jeg tilfældigt vægler et kort fra et blandet sæt. 00:03:24.619 --> 00:03:27.160 Lad os nu gøre det lidt mere spændende. 00:03:27.160 --> 00:03:29.250 eller måske er det lidt indlysende. 00:03:29.250 --> 00:03:32.130 Hvad er sandsynligheden for at jeg vælger 00:03:32.130 --> 00:03:38.540 noget der er en knægt og en hjeter? 00:03:42.120 --> 00:03:44.230 Jer der kender lidt til kort 00:03:44.230 --> 00:03:45.605 ved at der kun er 00:03:45.605 --> 00:03:47.900 et kort, der både en knægt og en hjerter. 00:03:47.900 --> 00:03:49.520 Det er hjerter knægt. 00:03:49.520 --> 00:03:50.530 00:03:50.530 --> 00:03:52.870 00:03:52.870 --> 00:03:56.200 00:03:56.200 --> 00:04:00.660 00:04:00.660 --> 00:04:02.630 00:04:02.630 --> 00:04:04.630 00:04:04.630 --> 00:04:07.650 00:04:07.650 --> 00:04:09.710 00:04:09.710 --> 00:04:12.640 00:04:12.640 --> 00:04:14.434 00:04:14.434 --> 00:04:16.600 00:04:16.600 --> 00:04:17.808 00:04:17.808 --> 00:04:20.019 00:04:20.019 --> 00:04:22.340 00:04:22.340 --> 00:04:25.350 00:04:25.350 --> 00:04:31.420 00:04:31.420 --> 00:04:33.050 00:04:33.050 --> 00:04:35.414 00:04:35.414 --> 00:04:36.830 00:04:36.830 --> 00:04:38.450 00:04:38.450 --> 00:04:39.872 00:04:39.872 --> 00:04:41.330 00:04:41.330 --> 00:04:43.579 00:04:43.579 --> 00:04:46.440 00:04:46.440 --> 00:04:49.912 00:04:49.912 --> 00:04:51.370 00:04:51.370 --> 00:04:57.010 00:04:57.010 --> 00:05:00.080 00:05:00.080 --> 00:05:02.650 00:05:02.650 --> 00:05:04.740 00:05:04.740 --> 00:05:06.820 00:05:06.820 --> 00:05:09.770 00:05:09.770 --> 00:05:13.730 00:05:13.730 --> 00:05:16.730 00:05:16.730 --> 00:05:20.860 00:05:20.860 --> 00:05:21.860 00:05:21.860 --> 00:05:24.490 00:05:24.490 --> 00:05:27.290 00:05:27.290 --> 00:05:28.520 00:05:28.520 --> 00:05:31.770 00:05:31.770 --> 00:05:33.460 00:05:33.460 --> 00:05:36.060 00:05:36.060 --> 00:05:38.505 00:05:44.310 --> 00:05:46.660 00:05:46.660 --> 00:05:51.560 00:05:54.270 --> 00:05:56.470 00:05:56.470 --> 00:05:58.540 00:05:58.540 --> 00:05:59.530 00:05:59.530 --> 00:06:03.540 00:06:03.540 --> 00:06:05.880 00:06:05.880 --> 00:06:06.920 00:06:06.920 --> 00:06:09.060 00:06:09.060 --> 00:06:12.870 00:06:12.870 --> 00:06:18.010 00:06:18.010 --> 00:06:19.530 00:06:22.180 --> 00:06:25.110 00:06:25.110 --> 00:06:27.380 00:06:27.380 --> 00:06:32.320 00:06:37.390 --> 00:06:39.210 00:06:39.210 --> 00:06:42.920 00:06:42.920 --> 00:06:45.470 00:06:45.470 --> 00:06:47.160 00:06:47.160 --> 00:06:50.810 00:06:50.810 --> 00:06:53.500 00:06:53.500 --> 00:06:56.600 00:06:56.600 --> 00:06:58.210 00:06:58.210 --> 00:06:59.710 00:06:59.710 --> 00:07:01.590 00:07:01.590 --> 00:07:03.325 00:07:11.040 --> 00:07:12.960 00:07:12.960 --> 00:07:15.670 00:07:15.670 --> 00:07:18.450 00:07:18.450 --> 00:07:20.260 00:07:20.260 --> 00:07:22.977 00:07:22.977 --> 00:07:25.060 00:07:25.060 --> 00:07:27.040 00:07:27.040 --> 00:07:29.950 00:07:29.950 --> 00:07:32.110 00:07:32.110 --> 00:07:35.580 00:07:35.580 --> 00:07:37.580 00:07:37.580 --> 00:07:41.100 00:07:41.100 --> 00:07:43.800 00:07:43.800 --> 00:07:46.047 00:07:46.047 --> 00:07:47.630 00:07:47.630 --> 00:07:52.580 00:07:52.580 --> 00:07:55.980 00:07:55.980 --> 00:08:00.170 00:08:00.170 --> 00:08:04.230 00:08:04.230 --> 00:08:06.239 00:08:06.239 --> 00:08:07.780 00:08:07.780 --> 00:08:09.370 00:08:09.370 --> 00:08:10.869 00:08:10.869 --> 00:08:13.890 00:08:13.890 --> 00:08:17.090 00:08:17.090 --> 00:08:21.090 00:08:21.090 --> 00:08:23.390 00:08:23.390 --> 00:08:24.990 00:08:24.990 --> 00:08:26.800 00:08:26.800 --> 00:08:29.130 00:08:33.919 --> 00:08:36.590 00:08:36.590 --> 00:08:38.090 00:08:38.090 --> 00:08:41.030 00:08:41.030 --> 00:08:43.730 00:08:43.730 --> 00:08:45.700 00:08:45.700 --> 00:08:47.260 00:08:50.340 --> 00:08:53.730 00:08:53.730 --> 00:08:56.530 00:08:56.530 --> 00:08:59.270 00:08:59.270 --> 00:09:01.270 00:09:01.270 --> 00:09:04.510 00:09:04.510 --> 00:09:10.200 00:09:10.200 --> 00:09:15.830 00:09:15.830 --> 00:09:20.370 00:09:20.370 --> 00:09:23.492 00:09:23.492 --> 00:09:24.950 00:09:24.950 --> 00:09:26.874 00:09:26.874 --> 00:09:28.040 00:09:28.040 --> 00:09:29.664 00:09:29.664 --> 00:09:31.230 00:09:31.230 --> 00:09:33.250 00:09:33.250 --> 00:09:35.260 00:09:35.260 --> 00:09:37.640 00:09:37.640 --> 00:09:40.284 00:09:42.850 --> 00:09:48.250 00:09:48.250 --> 00:09:51.890 00:09:51.890 --> 00:09:52.670 00:09:52.670 --> 00:09:55.330 00:09:55.330 --> 00:10:01.460