Transcript Making Predictions with Theoretical Probability

Making Predictions with
Theoretical Probability
Warm Up
In a standard 52-card deck, half of the cards are red and
half are black. The 52 cards are divided evenly into 4
suits: spades, hearts, diamonds, and clubs. Each suit has
three face cards (jack, queen, king), and an ace. Each suit
also has 9 cards numbered from 2 to 10.
1. Dawn draws 1 card, replaces it, and draws another
card. Is it more likely that she draws 2 red cards or
2 face cards?
2. Luis draws 1 card from a deck, 39 times. Predict
how many times he draws an ace.
3. Suppose a solitaire player has played 1,000 games.
Predict how many times the player turned over a
red card as the first card.
• You can make quantitative predictions based on
theoretical probability.
• You can use theoretical probabilities to make
qualitative predictions or compare how likely events
are.
• There is a connection between relative frequency and
probability.
• If you know the structure of the generating mechanism
of the probability experiment, you can approximate the
relative frequency of a series of random selections in a
quantitative or qualitative way using theoretical
probability.
• You can use mathematical models to generate the
possible non-overlapping outcomes of the probability
experiment and find the probabilities of the model.
To make predictions using theoretical probability
use the theoretical probability to write an
equation or use a proportion to make the
prediction for a given experiment.
Create a tree diagram to show the
outcomes and sample space for
flipping a coin and rolling a number
cube. Use the diagram to find the
probability of landing on heads and
getting a 6.
A bag contains same-size game pieces.
There are 6 purple pieces, 8 blue
pieces, and 5 green game pieces after
Geri removed one purple game piece
without looking. Find the theoretical
probability that the next game piece
Geri picks is the same color and the
probability that it is a different color.
Then explain whether it is likely that
the next game piece she picks will
match.
A spinner has eight equal sections
numbered from 1–8. Predict how
many times the pointer will land
on a multiple of 3 in 300 spins.
Blake volunteers at the animal
shelter. He has an equally likely
chance of being assigned to the
dog, cat, bird, or reptile section. If
he volunteers 30 times, about how
many times should he expect to be
assigned to the cat or reptile
section?
Lea pulls a blue tile out of a bag of
same-size tiles without looking. There
are 4 purple tiles, 6 blue tiles, and 8
green tiles left in the bag. Find the
theoretical probability that the next
tile she picks is the same color and the
probability that it is a different color.
Is it likely the next tile she picks will
match?
A company randomly assigns
employees four-digit security
codes using the numbers 1 through
4 to activate their e-mail accounts.
Any of the digits can be repeated.
Is it likely that more than 3 of the
1,280 employees will be assigned
the code 4113?
A bag contains 6 red marbles, 2
white marbles, and 1 gray marble.
You randomly pick out a marble,
record its color, and put it back in
the bag. You repeat this process 45
times. How many white or gray
marbles do you expect to get?
Horace is going to roll a standard
number cube and flip a coin. He
wonders if it is more likely that he rolls
a 5 and the coin lands on heads, or
that he rolls a 5 or the coin lands on
heads. Which event do you think is
more likely to happen? Find the
probability of both events to justify or
reject your initial prediction.
Exit Ticket
1. You roll a six-sided number cube 270 times.
Predict how many times you will roll a number
less than 3.
2. The equal sections of a spinner have one of the
following letters: A, B, A, C, B. Predict how many
times the pointer will land on a consonant in 60
spins.
3. In Kim’s homeroom, 4 students have no siblings,
9 students have 1 sibling, 8 students have 2
siblings, and 2 students have 3 or more siblings.
Is it likely that a student chosen at random will
have 2 or more siblings? Explain.
4. Drew rolls two number cubes 75 times. Is it
likely that she will get a sum of 3 more than 5
times? Explain.