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this is an assignment now, not an exam :)
In this experiment, you will be using two coins as a simulation for a real-world compound event. Suppose that a family has an equally likely chance of having a cat or a dog. If they have two pets, they could have 1 dog and 1 cat, they could have 2 dogs, or they could have 2 cats. 1. What is the theoretical probability that the family has two dogs or two cats? 2. Describe how to use two coins to simulate which two pets the family has. 3. Flip both coins 50 times and record your data in a table like the one below. Result Frequency Heads, Heads Heads, Tails Tails, Heads Tails, Tails Total 50 4. Based on your data, what is the experimental probability that the family has two dogs or two cats? 5. If the family has three pets, what is the theoretical probability that they have three dogs or three cats? 6. How could you change the simulation to generate data for three pets?
ok, first find 2 coins in your house somewhere
ok, keep them with you, we're going to need them pretty soon let's start with #1: the theoretical probability that the family will have two dogs or two cats first, the problem tells us that the probability of getting a dog and a cat are equally likely, so probability of a dog = 1/2 probability of a cat = 1/2 so, probability of two dogs = (probability of a dog)*(probability of a dog) = ?
right probability of two cats = (probability of a cat)*(probability of a cat) = ?
right, now we add the together to get our answer for #1: 0.25 + 0.25 = ?
right, let's move on to #2
we're going to use a coin to represent each pet. the probability of getting heads on a coin is 1/2 and tails is also 1/2, just like dog = 1/2 and cat = 1/2 so, we'll flip the coins one by one. a heads represents a dog and a tails represents a cat. so, as an example, if we flip heads on the first coin and tails on the second, that represents the family getting a dog and then a cat
that should be a sufficient answer for 2, just don't copy my words directly, ok?
ok i wont copy.. i put it in my words, dont worry.
ok next ! #3
do you understand what I wrote, though? this is important
yes i understand
#3 is asking you to do the simulation I just described take both coins, and flip them one at a time. now, take a look at each row of the table: Heads, Heads means the first coin is heads and the second coins is heads Heads, Tails means the first coin is heads and the second coin is tails Tails, Heads, means the first coin is tails and the second coin is heads Tails, Tails, means the first coin is tails and the second coin is tails
so, take your two coins. flip the first one, flip the second one, and tell me what you get for each one
i got heads and heads
right, so we put a tally mark in the first row, "Heads, Heads". now do the same thing 49 more times and fill out the table
read the problem...
it wants you to flip both coins 50 times
ok and then
so, we just flipped both coins once, and now we do the same thing 49 more times
but what do i put for frequency
frequency is the number of times you get for each of the 4 outcomes
so keep flipping the coins and keep track of how many times each outcome happens
oh i get it okay... give me 3 minutes to do it :)
make sure to stop at 50
i got ... 15 12 21 8
that adds up to 56 not 50
oh whoops.. hold on let me fix it
15 12 9 14
much better, now let's move on to #4
take a look at your table, and add together: Heads,Heads + Tails,Tails
now divide that by 50 and there's our answer
let's move to #5: probability of 3 cats or 3 dogs going back to what we said earlier... probability of cat = 1/2 probability of dog = 1/2 so probability of three dogs = (probability of dog)*(probability of dog)*(probability of dog) = ?
right probability of 3 cats = (probability of cat)*(probability of cat)*(probability of cat) = ?
now add them together 0.125 + 0.125 = ?
right, that's our answer for #5
for 6, all we need to do is use 3 coins instead of 2 coins, since we want 3 pets
and that should be it
ok so what do i do
whats number 6?
read the problem again then read what I wrote...
i dont get it
"How could you change the simulation to generate data for three pets?" our simulation used 2 coins and made data for 2 pets, so if we wanted 3 pets, we would use 3 coins instead of 2....
thats the answer?
pretty much, yes......