Transcript Topic # 5 - 5 : Theoretical vs Experimental Probability

Theoretical vs
Experimental
Probability
Experimental probability:
Probability based on a
collection of data.
• Will have a table of
results or data from the
experiment(s)!
What is the difference between
theoretical probability and
experimental probability?
• Theoretical probability shows
what should happen in an
experiment.
• Experimental probability
shows what actually
happened.
Jim tossed a coin 35 times. He recorded
whether the coin landed on heads or tails.
Use the results in the table to find each
experimental probability.
20 4

1. P (heads) =________
35 7
15 3

2. P (tails) = ________
35 7
HEADS
llll llll llll
llll
TAILS
llll llll llll
3.What is the theoretical probability of
throwing heads? 1
4. tails?
1
2
2
5. What is the difference between
the experimental probability of
throwing heads and the theoretical
probability of throwing heads?
(write answer as a percent rounded
to the nearest whole percent)
4 1 8 7 1
   
7 2 14 14 14
Experimental - theoretical
This is
about 7%
6. What is the difference between
the experimental probability of
throwing tails and the theoretical
probability of throwing tails?
(write answer as a percent rounded
to the nearest whole percent)
1 3 7 6 1
   
2 7 14 14 14
Theoretical - Experimental
This is
about 7%
Mrs. Smith has a bag that contains 6 red
Lifesavers, 5 yellow Lifesavers, 8 orange Lifesavers
and 9 white Lifesavers. She has another bag that
contains 3 Butterfingers, 6 Snickers, and 4 Hershey
Bars. You are a student that is being rewarded for
good behavior so you get to draw a piece of candy
from each bag. Find the following probabilities.
7.P(yellow Lifesaver, a Snickers)
5 6
15


28 13 182
 8%
8.P(red or orange Lifesaver, a Hershey Bar)
6  8 4 14 4
2



  15%
28 13 28 13 13
9. P(no white lifesaver, a Butterfinger)
8  5  6 3 19 3
57
 16%


 
28
13 28 13 364
David rolled a number cube, with the
numbers 1-6 on it. He recorded the
results in the table below.
1
IIII
Find the THEORETICAL
probabilites:
2
III
1/6
10) P(4) = ______________
3
IIII
Number
Outcomes
4
IIII I
5
II
6
I
½
11) P(odd number) = __________
12) P(2 or 5) = 1/3
__________
13) P(a factor of 3) =1/3
_________
14) What is the difference between the experimental probability of
rolling a 2 or 5, and the theoretical probability of rolling a 2 or 5?
1/3 – 1/4 = 1/12