### 3 - Experimental & Theoretical Probability

```P.O.D. #3
basic
You spin the spinner above
and flip a coin. Determine
the probability of spinning a
2 and flipping tails?
Mr. & Mrs. Romero are
expecting triplets. Determine
the probability that they will
have two boys and one girl.
Sample Space: 1H, 1T, 2H,
2T, 3H, 3T, 4H, 4T, 5H, 5T
Sample Space: GGG, GGB, GBG,
GBB, BGG, BGB, BBG, BBB
1
P(2,tails) =
10
3
P(2B, 1G) =
8
Theoretical & Experimental Probability
Theoretical probability is the ratio of the number of ways
an event can occur to the number of possible outcomes.
Experimental probability is an estimated probability
based on the relative frequency of positive outcomes
occurring during an experiment.
Theoretical probability is based on what should happen
when conducting a probability experiment.
Experimental probability is based on what actually
occurred during an experiment.
Theoretical and experimental probability can be used to
Example:
Last month a DVD store sold 67 action DVDs, 58 comedy DVDs,
45 drama DVDs, and 30 horror DVDs. If the store expects to
sell 500 DVDs this month, how many comedy DVDs should
they expect to sell?
P(comedy) =
58 = 29
200
100
The store should expect to
sell 145 comedy DVDs.
29
c
=
100
500
29  500 = 100  c
14,500 = 100c
÷100 ÷100
145 = c
Whiteboard:
A coin is tossed 50 times, and it lands on heads 28 times. Find the
experimental probability and the theoretical probability of the coin
landing on heads. Then, compare the experimental and theoretical
probabilities.
1. Find the experimental probability of the coin landing on
2. Find the theoretical probability of the coin landing on
3. Compare the experimental and theoretical
probabilities.
Whiteboard:
A coin is tossed 50 times, and it lands on heads 28 times.
1. Find the experimental probability of the coin landing on heads.
2. Find the theoretical probability of the coin landing on heads.
3. Compare the experimental and theoretical probabilities.
Experimental Probability:
28
= 56%
50
Theoretical Probability:
1
= 50%
2
Compare:
The experimental probability
is 56%, which is close to the
theoretical probability of
50%.
Whiteboard:
Yesterday, 50 bakery customers bought muffins and 11 of those
customers bought banana muffins. If 100 customers buy muffins
tomorrow, how many would you expect to buy a banana muffin?
11 = b
50 100
11  100 = 50  b
1100 = 50b
÷50 ÷50
22 = b
I would expect 22 customers to buy
a banana muffin.
```