Coins
Probability of getting tails on a fair coin
1/2
50%
0.5
The probability of rolling a 4 on a normal dice is
1/6
about 17%
John rolls a dice 2 times and gets 6 every time
Is the dice fair or rigged?
Not enough data to say
What could be a good way to simulate a basketball player who shoots 50% free throws?
a coin
(or other method that is about 50%)
If you pick a face card from a deck of cards you don't have to wash the dishes. Is that fair?
No, you're more likely to wash the dishes
12/52 face cards is not 50/50
In an unfair coin what is the probability of getting heads?
NOT 50%
unfair means NOT equally likely
The probability of rolling an even number on a dice is
3/6 or 1/2 or 0.5
{2,4,6}/{1,2,3,4,5,6}
John rolls a dice 10 times and gets 6 every time.
Is the dice fair or rigged?
maybe, but not enough data yet to be sure
Shaq shot 42% free throws for Miami. Would rolling a dice and only letting 6 be making a shot be a good simulation?
No, 1/6 is 17%, which is not close to 42%
If you flip a quarter and get heads 3 times in a row you get a homework pass. Is that fair?
No HHH is 1/8 which is not 50%
Make a tree diagram for flipping a coin twice
The probability of rolling a prime number on a 7 sided dice is
4/7
{2,3,5,7}/{1,2,3,4,5,6,7}
John rolls a dice 50 times and gets 6 every time
Is the dice fair or rigged?
more than 99% chance that its unfair
Why would someone want to do a simulation?
faster, easier, cheaper than the real experiment
to make a prediction
If you pick a prime number from 1-8 you get a homework pass. Is that fair?
Yes
{2,3,5,7}/{1,2,3,4,5,6,7,8} = 50%
If you flip a coin 100 times and get heads 58 times and tails 42 times should you believe it is a fair coin?
More likely to be fair because it's close to 50/50
When you roll 2 dice what is the most common outcome?
7 because most possible ways to get it
you can get (1,6) , (2,5) , (3,4) , (4,3) , (5,2) , (6,1)
John rolls a dice 600 times and gets 6 103 times
Is the dice fair or rigged?
that's about what we'd expect so probably fair
Why would you make 10,000 simulations instead of 5
Law of large numbers:
More tries gets more accurate results
To split up a cookie between 2 people one person cuts it into 2 pieces and then the other person chooses the piece they want
Yes
if player 1 makes an uneven cut then player 2 gets to pick the larger piece
If you flip a coin 100 times and get 63 heads and 57 tails what is a possible mistake you made in your procedure?
total heads and tails should equal 100, but 63+57 = 110
In the game monopoly should you try to get the first two purple properties?
No the chances of landing on them is very low
What is the largest integer?
trick question, there isn't one
Joe simulated the Eagles season 10,000 times. Why?
If you randomly pick a prime number between 1 and n you a get a 3 on the quiz
No not fair:
((n)/(log n))n < 50%
Or this question is not fair, we didn't learn that.