00:00 in this video we're going to focus on
00:02 probability word problems a jar contains
00:06 seven red marbles six green marbles five
00:09 blue marbles and two yellow marbles what
00:12 is the probability of selecting a green
00:14 marble well let's make a list of the
00:18 different colors that we have so we have
00:19 red we have green blue and we have
00:26 yellow so there are seven red marbles
00:31 six green marbles five blue marbles and
00:35 two yellow marbles now let's add up
00:38 these numbers 7 plus 6 is 13 13 plus 5
00:42 is 18 18 plus 2 is 20 so there's a total
00:46 of 20 marbles in the jar now if you want
00:50 to calculate the probability of getting
00:53 let's say a green marble what you need
00:57 to do is find the number of green
01:00 marbles in the jar there's six green
01:03 marbles and divided by the total number
01:05 of marbles which is 20 so the
01:09 probability is six out of 20 but of
01:11 course we can reduce the fraction since
01:14 both numbers are even we can divide them
01:16 by 2 half of 6 is 3 half of 20 is 10 3
01:21 over 10 is basically point three as a
01:23 decimal which is equal to 30 percent so
01:28 there's a 30 percent chance of selecting
01:30 a green marble from this jar now what
01:34 about the blue marble what is the
01:37 probability of selecting the blue marble
01:41 so how many blue marbles are in the jar
01:43 notice that we have five in the jar out
01:46 of 20 so the probability is 5 over 20 so
01:52 now let's reduce the fraction by
01:56 dividing each number by 5 5 divided by 5
02:02 is 120 divided by 5 is 4 1 over 4 if you
02:06 type it in the calculator is 0.25 as a
02:10 decimal which correlates to 25%
02:13 so there's a 25% chance of selecting a
02:17 blue marble now if there's a 25% chance
02:21 of selection of a blue marble and what
02:24 is the probability of not selecting a
02:26 blue marble to find the probability of
02:30 not selecting a blue marble it's going
02:36 to be one the mine is the probability of
02:41 selecting a blue marble and is the the
02:44 probability of selecting blue marble is
02:47 0.25 1 minus 0.25 is equal to 0.75 which
02:52 is 75% so this is a 25% chance of
02:59 selecting a blue marble then there's a
03:01 75% chance of not selecting a blue
03:04 marble if there's a 30% chance of
03:07 selecting a green marble then there's a
03:10 70% chance of not selecting a green
03:20 let's clear away a few things now let's
03:23 talk about another way in which we can
03:25 calculate the probability of not
03:28 selecting a green marble
03:38 the other technique involves finding how
03:41 many marbles are not green so we have 7
03:45 5 & 2 so that 7 plus 5 is 12 12 plus 2
03:51 is 14 so there are 14 marbles that are
03:56 not green out of a total of 20 and so
04:00 let's go ahead and reduce this fraction
04:02 so let's divide both numbers by 2 14
04:09 divided by 2 is 7 20 divided by 2 is 10
04:13 and so we get 7 out of 10 which is point
04:18 7 and point 7 if you multiply by 100
04:22 this will give you 70% so as you can see
04:26 there's a 7 percent chance of not
04:29 selecting a green marble now let's get
04:41 now let's move on to the next part parts
04:43 gene what is the probability of
04:45 selecting a green or a yellow marble how
04:50 can we figure this out if you see an or
04:52 statement its associated with the sum
04:56 the probability of selecting a green or
04:58 yellow marble is equal to the
05:01 probability of selecting a green marble
05:05 plus the probability of selecting a
05:09 yellow marble so we just got to add
05:14 these two values and it's going to give
05:16 us the answer so there are six green
05:18 marbles out of a total of twenty and to
05:25 find the probability of selecting a
05:26 yellow marble we can see that there are
05:28 two yellow marbles in the jar of twenty
05:31 marbles so it's two over twenty now
05:34 since the denominators are the same in
05:36 these two fractions we can go ahead and
05:38 add them six plus two is eight so it's
05:41 eight over twenty now eight and twenty
05:45 are divisible by four so let's reduce
05:47 the fraction so this is going to be 2
05:49 over 5 if you type 2/5 in your
05:53 calculator or if you use long division
05:55 you can convert this fraction into a
05:57 decimal and so it's going to be 0.4
05:59 which is 40 percent so there's a 40
06:04 percent chance of getting a green or a
06:09 yellow marble now what about the next
06:13 part what is the probability of getting
06:19 a red marble and then a blue marble with
06:23 replacement so this is basically an and
06:27 statement we need to get red and blue on
06:30 the first try we need to get red and on
06:33 the second try we need to get blue so
06:36 the order matters you so what is the
06:40 probability of getting a red marble on
06:43 the first try by the way whenever you
06:45 have an and statement you need to
06:50 if there's an or you need to add so just
06:54 keep that in mind so we need to multiply
06:57 the probability again a red marble times
07:00 the probability of getting a blue marble
07:08 so what is the probability of getting a
07:11 red marble on the first try so there's
07:14 seven red marbles out of a total of
07:16 twenty so it's seven over twenty now
07:22 what is the probability of selecting a
07:24 blue marble with replacement what
07:27 replace that means that once you take
07:29 out the red marble in the first try you
07:31 put it back in and then you want to see
07:33 you know the chances of getting the blue
07:35 marble on the second try so once you put
07:37 the red model back in there's still a
07:39 total of twenty blue marbles and there's
07:42 five I mean there's a total of twenty
07:44 marbles in general and out of those
07:47 twenty marbles we have five blue marbles
07:49 I think I said twenty blue marbles with
07:52 there's only five so once you put the
07:55 red marble back in you still have twenty
07:57 marbles in the jar now instead of
08:01 multiplying across let's cancel first we
08:09 can reduce five over twenty and we can
08:12 divide each number by five so we can
08:16 cancel five from the top and the bottom
08:17 so this is going to be 1 over 4 7 times
08:21 1 is 7 4 times 20 is 80 so the answer is
08:26 7 over 80 and as a decimal this is equal
08:32 to point zero eight seven five which is
08:38 eight point seven five percent
08:45 now if you're wondering what just
08:47 happened I accidentally closed the
08:51 application and so I'm just going to
08:55 rewrite this information so let's work
08:58 on the next part what is the probability
09:02 of selecting a red marble and then a
09:05 blue marble but this time without
09:07 replacement so what do you think we have
09:11 to do here feel free to pause the video
09:13 and work on that example so we're still
09:17 done with multiplication there's two
09:20 events we need to get a red marble and a
09:23 blue marble and anytime you're dealing
09:26 with an and statement in regards to
09:28 probability you need to multiply the two
09:30 events together that is you need to
09:33 multiply the probability of getting
09:35 those two events so we need to get a red
09:37 marble on the first try and then a blue
09:41 marble on the second try so the
09:46 probability of getting a red marble on
09:48 the first try is still seven over twenty
09:50 so that part hasn't changed now what
09:54 about the probability of getting a blue
09:56 marble but without replacing without one
10:00 place that means that after you take out
10:02 the first red marble on the first try
10:05 you don't put it back in it stays
10:08 outside of the charm which means that we
10:11 no longer have twenty marbles in the jar
10:14 we now have 19 so therefore the
10:18 probability of selecting a blue marble
10:23 since there's five blue marbles in the
10:25 jar that contains only 19 marbles left
10:28 over and so this is going to give us the
10:32 answer 20 is basically five times four
10:37 and notice that we can cancel a 5 which
10:43 will make the math a lot easier so now
10:47 on top is just going to be a 7 on the
10:50 bottom 4 times 19 4 times 19 is 76
10:58 7/7 t6h point is zero nine - so there's
11:06 a 9.2 percent chance of again a red
11:09 marble on the first try and then a blue
11:12 marble on its second try without
11:25 now what about the last one what is the
11:28 probability of selecting a red marble
11:31 and a blue marble without replacement so
11:36 how is Part F different than party go
11:42 ahead pause the video and think about
11:44 this problem see if you can get the
11:45 answer try to work it out and then when
11:48 you're ready unpause the video and see
11:50 what the solution is so what's the
11:52 difference between then and and now in
11:58 Part II on the first try you want to get
12:01 a red marble and on the second try you
12:06 want to get a blue marble in that order
12:10 but in Part F the order is not specified
12:14 so that means that you can get a red
12:18 marble in the first try and then the
12:20 blue marble in the second shrine or
12:22 remember or means plus or some you can
12:26 get a blue marble on the first try and
12:29 then a red marble on the second try in
12:34 Part F because the order is not
12:36 specified it can be Rd or Br so the
12:43 probability of getting red on the first
12:44 try and then blue on the second try we
12:47 got that answer in the last problem it's
12:50 7 over 24 the red marbles and then for
12:53 the blue marbles it's 5 over 19 this is
12:57 without replacement so don't forget to
13:00 deduct this number by 1 now for B are
13:05 the probability of getting a blue marble
13:07 on the first try there's five blue
13:09 marbles out of a total of 20 and since
13:12 it's without replacement once we take
13:14 out the blue marble there's 19 less and
13:17 the probability of selecting a red
13:19 marble is going to be 7 out of the
13:21 remaining 19 to notice that these two
13:24 answers are the same
13:29 in both cases we're going to get the
13:31 same answer of 7 over 76 that's the
13:35 probability of getting red then blue and
13:36 the probability of getting blue then red
13:38 is also 7 out of 76 you have to double
13:42 the answer so it's 14 out of 76 now we
13:48 can be deuce this fraction we can divide
13:50 the top and the bottom by 2 so this is
13:52 going to turn into 7 over 38 738 I mean
14:00 7 over 38 that's a point 1 8 4 as a
14:04 decimal so there's an 18 point 4 percent
14:07 chance of getting a red and a blue
14:11 marble without replacement the
14:16 probability of not getting a red and a
14:19 blue marble without replacement is 100 -
14:21 eighteen point four and that's 81 point
14:26 six percent chance of Nagin a red and
14:30 blue so now let's review a few important
14:34 details that's going to help you when
14:38 solving probability problems so anytime
14:41 you see the word or associate it with
14:43 addition or some whenever you see the
14:47 word and associate it with
14:50 multiplication so just keep that in mind
14:56 so here's a question see what is the
15:00 probability of selecting a red marble
15:03 then a green novel not and so you want
15:08 to get a red marble first and then a
15:10 green marble on a second try or get in a
15:16 blue marble and then a yellow marble on
15:21 the second try so go ahead and try to
15:25 figure this out so the probability of
15:28 getting red and green we need to
15:32 multiply so it's going to be P of R as
15:35 the probability of selecting a red
15:36 marble and the probability of selecting
15:40 green marble so we're going to multiply
15:43 and then we have an or statement so
15:45 that's going to be addition the
15:49 probability is getting a blue marble
15:50 that's P B and the probability of again
15:55 the yellow marble we'll call it a py so
16:00 we're going to have to multiply it by py
16:10 the probability of again a red marble is
16:12 7 over 20 and let's say it's with
16:18 replacement I forgot to specify that so
16:22 with replacement does a nominative will
16:24 remain 20 so there's six green marbles
16:28 out of a total of twenty and then plus
16:30 the probabilities again a blue marble is
16:32 five over twenty and again a yellow
16:35 marble it's two over twenty
16:40 now let's reduce the fractions that we
16:42 have we can add them right now if we
16:45 want to so you can reduce it now or you
16:48 can add 6 times 7 is 42
16:52 let's Adam first 20 times 20 is 400 5
16:58 times 2 is 10 so this is going to be 10
17:02 out of 400 42 plus 10 is 52 so it's 50
17:09 two out of 400 now we can divide both
17:12 numbers by 4 52 divided by 4 is 13 400
17:18 divided by 4 is 113 over 100 it's easy
17:25 to see what the decimal value of that is
17:27 that's point 13 which is 13% and so
17:36 that's the answer that's the probability
17:39 of getting a red marble on the first try
17:45 then a green marble on the second try or
17:48 getting a blue marble on the first try
17:50 and then a yellow marble on the second
17:52 try so that's it for this video
17:55 hopefully it's been helpful for you in
17:58 dealing with probability problems so
18:01 thanks for watching and have a great day
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