Transcript xabst binary waves

Bellwork
1. What fraction of the
spinner is blue? Write in
simplest form.
2. Suppose you spin. Are
your chances of landing on
a blue space the same as
landing on a red space?
Support your answer.
3. Suppose you spin it twice.
If the first time you land on
a green space, does it
impact your chances of
landing on a green space
the second time?
Bellwork - ANSWERS
1. What fraction of the spinner is
blue? Write in simplest form.
3/
12 = ¼
2. If you spin the spinner, are your
chances of landing on a blue
space the same as landing on a
red space? Support your answer.
No. There are only 3 blue spaces, while there
are 5 red spaces. The chances of landing
on blue are 3 out of 12, while the chances
of landing on red are 5 out of 12.
Therefore, the chances of landing on a
red space are greater than landing on a
blue space.
Bellwork – ANSWERS continued
3. Suppose you spin it twice. If the
first time you land on a green
space, does it impact your
chances of landing on a green
space the second time? Support
your answer.
No. The number of green spaces and total
spaces does not change from the first
spin to the second – these events are
independent from one another. Therefore
the chances of landing on a green space
the second time are the same as the first
time.
Probability
Cornell Notes with Summary
Essential Question: What is the
difference between an outcome
and an event and how are they
related to probability?
Events
• Probability – the chance of an event
happening expressed as a ratio with a
value between 0 and 1.
– What is the probability of rolling a 4 on a
regular number cube?
• Since there is only 1 four, and 6 sides, the
probability is 1 out of 6, or 1/6
• The probability of rolling a 4 expressed as a
decimal is .17
• Outcome – any possible result of an action
Multiple Events
– The probability of one event OR another is
found by adding the probability of the first to
the second
• P(A or B) = P(A) + P(B)
– The probability of one event AND / THEN
another is found by multiplying the
probability of the first to the second (making
adjustments if they are dependent events)
• P(A and B) or P(A then B)
– Independent = P(A x B)
– Dependent = P(A x B following A)
You Try It!
• Find the probability of choosing a spade from a deck
of cards, replacing it, AND then choosing an ace as
the second card.
• P (spade) = 13 spades = 1 *always simplify*
52 cards
4
• P (ace) = 4 aces = 1 *always simplify*
52 cards
13
• P (spade and ace) = 1/4 x 1/13 = 1/52
• The probability of choosing a spade from a deck of cards,
replacing it, and then choosing an ace as the second card
is 1 out of 52.
You Try It!
• Find the probability of choosing a king from a deck of cards, *not*
replacing it, AND then choosing a jack as the second card.
• P (king on first pick) = 4 kings = 1 *always simplify*
52 cards
4
• P (jack given king on first pick) = 4 jacks *in simplest form*
51 cards
Remember, you kept the card from the first pick, so now there are
only 51 cards left in the deck.
• P (king, and then jack) = 1/4 x 4/51 = 4/52
•
The probability of choosing a spade from a deck of cards, replacing it,
and then choosing an ace as the second card is 1 out of 52.
Likelihood of Events
• Everything has probability, but not
everything is likely.
• Probability is represented as a ratio of:
desired outcomes
total possible outcomes
• Likelihood is where that probability lies
between 0 and 1, where 0 is unlikely and 1
is likely.
Likelihood of Events - Likely
• If something is LIKELY, then the probability
of it happening is closer to 1.
– The probability of landing on a blue space on
a spinner with 5 spaces with 1 red space, 1
yellow space, and 3 blue spaces is 3/5,
therefore landing on a blue space is likely.
Likelihood of Events – Unlikely
• If something is UNLIKELY, then the
probability of it happening is closer to 0.
– The probability of rolling a 3 on a regular
number cube is 1/6, therefore rolling a 3 on a
regular number cube is unlikely.
Likelihood of Events – Neither
• If something has a 50/50 chance of
happening, it is NEITHER likely nor
unlikely.
– For instance, the probability of tossing a head
or a tail on a coin is ½ for heads and ½ for
tails. Therefore, tossing heads is neither likely
nor unlikely.
You Try It!
• Find the probability of choosing a king from a deck of cards OR
choosing a spade. State if it is a likely, unlikely, or neither likely nor
unlikely event.
• P (king) = 4 kings = 1 *in simplest form*
52 cards
13
• P (spade) = 13 spades = 1 *in simplest form*
52 cards
4
• P (king or spade) = 1/13 + 1/4 = **common denominator needed**
4/
13/
17/
52 +
52 =
52
•
The probability of choosing a king or spade from a deck of cards is 17
out of 52 for one draw; therefore, it is UNLIKELY that you will choose a
king or spade.
Summary
• Answer the Essential Question in two or
more complete sentences.
• EQ: What is the difference between an
outcome and an event and how are they
related to probability?
HOMEWORK
• Find the probability of the following:
1. Drawing all spades from a deck of cards
after 5 draws if you replace the cards each
time.
2. Rolling a 4 or an odd number on a regular
number cube.
3. Drawing all jacks from a deck of cards and
not 5 on a regular number cube.
• Then, state whether each is likely, unlikely,
or neither likely nor unlikely to occur.
Exit Ticket
1. Find P(3 or 5) on a number cube.
2. Susie rolls a regular number cube - is it
likely, unlikely, or neither likely nor unlikely
that she rolls an even number?
3. Bob draws a card from a deck, keeps the
card, and then draws another - is it likely,
unlikely, or neither likely nor unlikely that he
draws a spade and a 7?
Exit Ticket - ANSWERS
1.
Find P(3 or 5) on a number cube. 1/6 + 1/6 = 2/6 = 1/3
2.
Susie rolls a regular number cube - is it likely, unlikely, or
neither likely nor unlikely that she rolls an even number?
neither likely nor unlikely since the probability of rolling
an even number is 3/6 = 1/2
3.
Bob draws a card from a deck, keeps the card, and then
draws another - is it likely, unlikely, or neither likely nor
unlikely that he draws a spade and a 7? the probability of
drawing a spade is 13/52 and the probability of drawing
a seven is 4/51 (he kept the card after the first draw).
Multiplying the fractions, we end up with a probability of
52/2652 (or 1/52 if simplified), which is an unlikely result