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  • 00:00

    An American roulette wheel has 38 slots.
    An American roulette wheel has 38 slots.

  • 00:02

    Two slots are numbered zero and double zero,
    Two slots are numbered zero and double zero,

  • 00:05

    and the remaining slots anyone numbered from one through 36.
    and the remaining slots anyone numbered from one through 36.

  • 00:08

    For some additional information,
    For some additional information,

  • 00:09

    a roulette wheel looks more like this
    a roulette wheel looks more like this

  • 00:11

    where there are 38 slots,
    where there are 38 slots,

  • 00:13

    18 are red, 18 are black, and two are green,
    18 are red, 18 are black, and two are green,

  • 00:17

    and the numbers are double zero, zero,
    and the numbers are double zero, zero,

  • 00:19

    and then one through 36.
    and then one through 36.

  • 00:20

    The way the game works,
    The way the game works,

  • 00:21

    the wheel spins and a ball bounces around.
    the wheel spins and a ball bounces around.

  • 00:25

    As the wheel slows, a ball lands in one of the slots,
    As the wheel slows, a ball lands in one of the slots,

  • 00:28

    which determines who wins and who loses.
    which determines who wins and who loses.

  • 00:32

    For our questions, though,
    For our questions, though,

  • 00:33

    we'll use the table here on the right
    we'll use the table here on the right

  • 00:35

    that shows all the possible outcomes for the roulette wheel.
    that shows all the possible outcomes for the roulette wheel.

  • 00:39

    This is actually the table where people place bets.
    This is actually the table where people place bets.

  • 00:42

    First question is what are the odds
    First question is what are the odds

  • 00:43

    for the ball landing in an odd-numbered slot?
    for the ball landing in an odd-numbered slot?

  • 00:46

    Remember, the odds in favor of an event are equal
    Remember, the odds in favor of an event are equal

  • 00:49

    to the ratio of the number of favorable outcomes
    to the ratio of the number of favorable outcomes

  • 00:52

    to the number of unfavorable outcomes.
    to the number of unfavorable outcomes.

  • 00:56

    Looking at the outcomes of the roulette wheel,
    Looking at the outcomes of the roulette wheel,

  • 00:59

    the numbers one through 36, half of them will be odd.
    the numbers one through 36, half of them will be odd.

  • 01:02

    Remember, odd numbers are numbers
    Remember, odd numbers are numbers

  • 01:04

    like one, three, five, seven, and so on.
    like one, three, five, seven, and so on.

  • 01:07

    Let's go ahead and mark all of the odd numbers.
    Let's go ahead and mark all of the odd numbers.

  • 01:10

    One, three, five, seven, nine,
    One, three, five, seven, nine,

  • 01:14

    11, 13, 15, 17, 19,
    11, 13, 15, 17, 19,

  • 01:19

    21, 23, 25, 27, 29,
    21, 23, 25, 27, 29,

  • 01:23

    31, 33, and 35.
    31, 33, and 35.

  • 01:26

    There are a total of 18 odd numbers on the roulette wheel,
    There are a total of 18 odd numbers on the roulette wheel,

  • 01:30

    and therefore there are 18 favorable outcomes
    and therefore there are 18 favorable outcomes

  • 01:33

    for the ball landing in an odd-numbered slot.
    for the ball landing in an odd-numbered slot.

  • 01:35

    Let's record this below.
    Let's record this below.

  • 01:39

    And because there are 38 slots,
    And because there are 38 slots,

  • 01:41

    there are always a total of 38 possible outcomes
    there are always a total of 38 possible outcomes

  • 01:43

    on the roulette wheel,
    on the roulette wheel,

  • 01:46

    which also means the number of unfavorable outcomes
    which also means the number of unfavorable outcomes

  • 01:49

    must be 38 minus 18, which is 20.
    must be 38 minus 18, which is 20.

  • 01:52

    There are 20 numbers on the roulette wheel that are not odd.
    There are 20 numbers on the roulette wheel that are not odd.

  • 01:56

    And now to find the odds for the ball landing
    And now to find the odds for the ball landing

  • 01:58

    in an odd-numbered slot,
    in an odd-numbered slot,

  • 02:00

    again, this is the ratio of the number of favorable outcomes
    again, this is the ratio of the number of favorable outcomes

  • 02:03

    to the number of unfavorable outcomes,
    to the number of unfavorable outcomes,

  • 02:06

    which will be 18 to 20.
    which will be 18 to 20.

  • 02:08

    But let's first write the ratio in fraction form
    But let's first write the ratio in fraction form

  • 02:10

    because we can simplify ratios just like fractions.
    because we can simplify ratios just like fractions.

  • 02:15

    So 18 and 20 share a common factor of two.
    So 18 and 20 share a common factor of two.

  • 02:18

    To simplify the ratio, we divide both by two.
    To simplify the ratio, we divide both by two.

  • 02:23

    18 divided by two is nine, 20 divided by two is 10,
    18 divided by two is nine, 20 divided by two is 10,

  • 02:28

    which gives us a ratio of nine to 10 in fraction form
    which gives us a ratio of nine to 10 in fraction form

  • 02:32

    which we can also write using the word to
    which we can also write using the word to

  • 02:35

    and also using a colon.
    and also using a colon.

  • 02:39

    Next, what are the odds against the ball landing
    Next, what are the odds against the ball landing

  • 02:41

    in an odd-numbered slot?
    in an odd-numbered slot?

  • 02:43

    The odds against an event are equal to the ratio
    The odds against an event are equal to the ratio

  • 02:46

    of the number of unfavorable outcomes
    of the number of unfavorable outcomes

  • 02:48

    to the number of favorable outcomes.
    to the number of favorable outcomes.

  • 02:51

    And since we already know the odds in favor
    And since we already know the odds in favor

  • 02:53

    of the ball landing in an odd-numbered slot are nine to 10,
    of the ball landing in an odd-numbered slot are nine to 10,

  • 02:57

    the odds against landing
    the odds against landing

  • 02:58

    on an odd-numbered slot must be 10 to nine.
    on an odd-numbered slot must be 10 to nine.

  • 03:09

    The original ratio would have been 20 to 18,
    The original ratio would have been 20 to 18,

  • 03:12

    which again would simplify to 10 to nine.
    which again would simplify to 10 to nine.

  • 03:15

    Next, what are the odds for the ball landing
    Next, what are the odds for the ball landing

  • 03:17

    in the zero or double zero slot?
    in the zero or double zero slot?

  • 03:19

    Going back to the table,
    Going back to the table,

  • 03:21

    there are only two favorable outcomes
    there are only two favorable outcomes

  • 03:23

    getting a zero or a double zero.
    getting a zero or a double zero.

  • 03:26

    So we have two favorable outcomes,
    So we have two favorable outcomes,

  • 03:28

    again, out of a total of 38 outcomes,
    again, out of a total of 38 outcomes,

  • 03:31

    and therefore the number of unfavorable outcomes
    and therefore the number of unfavorable outcomes

  • 03:34

    or the slots that are not zero or double zero are 36,
    or the slots that are not zero or double zero are 36,

  • 03:38

    which we can also find by subtracting two from 38.
    which we can also find by subtracting two from 38.

  • 03:41

    [person speaking faintly]
    [person speaking faintly]

  • 03:43

    So the odds in favor for the ball landing
    So the odds in favor for the ball landing

  • 03:45

    in the zero or double zero slot are two to 36.
    in the zero or double zero slot are two to 36.

  • 03:50

    Again, the ratio of the number of favorable outcomes
    Again, the ratio of the number of favorable outcomes

  • 03:53

    to the number of unfavorable outcomes.
    to the number of unfavorable outcomes.

  • 03:56

    But again, notice how this ratio does simplify.
    But again, notice how this ratio does simplify.

  • 03:59

    Both share a common factor of two.
    Both share a common factor of two.

  • 04:02

    And therefore the simplified odds are one to 18.
    And therefore the simplified odds are one to 18.

  • 04:13

    And for the last question,
    And for the last question,

  • 04:14

    what are the odds against for the ball landing
    what are the odds against for the ball landing

  • 04:16

    on the zero or double zero?
    on the zero or double zero?

  • 04:19

    Well, if the odds in favor are one to 18,
    Well, if the odds in favor are one to 18,

  • 04:21

    the odds against are going to be 18 to one.
    the odds against are going to be 18 to one.

  • 04:32

    I hope you found this helpful.
    I hope you found this helpful.

All

Determine Odds of a Roulette Wheel

13,488 views

Mathispower4u

Video Language:

  • English

Caption Language:

  • English (en)

Accent:

  • English (US)

Speech Time:

85%
  • 3:56 / 4:37

Speech Rate:

  • 174 wpm - Fast

Category:

  • Education

Tags :

Intro:

An American roulette wheel has 38 slots.. Two slots are numbered zero and double zero,. and the remaining slots anyone numbered from one through 36.
For some additional information,. a roulette wheel looks more like this. where there are 38 slots,. 18 are red, 18 are black, and two are green,. and the numbers are double zero, zero,. and then one through 36.. The way the game works,. the wheel spins and a ball bounces around.. As the wheel slows, a ball lands in one of the slots,
which determines who wins and who loses.. For our questions, though,. we'll use the table here on the right. that shows all the possible outcomes for the roulette wheel.
This is actually the table where people place bets.
First question is what are the odds. for the ball landing in an odd-numbered slot?. Remember, the odds in favor of an event are equal.

Video Vocabulary

question

/ˈkwesCH(ə)n/

noun verb

sentence worded or expressed so as to elicit information. To ask for or try to get information.

numbers

/ˈnəmbər/

noun other verb

arithmetical value expressed by word, symbol, or figure. Particular songs or dances performed during shows. To claim to be part of a larger group, series, set.

landing

/ˈlandiNG/

noun verb

instance of coming to land. To arrive or cause a boat to arrive at the shore.

determines

/dəˈtərmən/

verb

To establish the facts about; discover.

possible

/ˈpäsəb(ə)l/

adjective noun

Being able or appropriate for a task or purpose. candidate for job.

additional

/əˈdiSH(ə)n(ə)l/

adjective

added, extra, or supplementary to what is already present or available.

favorable

/ˈfāv(ə)rəb(ə)l/

adjective

expressing approval.

numbered

/ˈnəmbər/

verb

To assign a sequence within a group, series, set.

bounces

/bouns/

noun verb

rebound of ball. To move energetically in an up and down motion.

unfavorable

/ˌənˈfāv(ə)rəb(ə)l/

adjective

Not encouraging or approving or pleasing.

remaining

/rəˈmāniNG/

adjective verb

(Those things) not yet done. To stay in a place when other people have gone.

actually

/ˈak(t)SH(o͞o)əlē/

adverb

as truth or facts.

roulette

/ro͞oˈlet/

noun verb

gambling game in which ball is dropped on to revolving wheel with numbered compartments. make slit-shaped perforations in.

outcomes

/ˈoutˌkəm/

noun other

way thing turns out. Some things that happen as a result, consequences.

through

/THro͞o/

adjective adverb preposition

From one end or side of something to the other. expressing movement into one side and out of other side of opening etc.. Allowing you to pass between, or to.