LESSON 2 – THEORETICAL PROBABILITY
THEORETICAL PROBABILITY
𝑃 (𝐸 ) =
𝑛(𝐸)
𝑛(𝑆)
Where 𝑛(𝐸) is the # of outcomes in the event and
𝑛(𝑆) is the # of outcomes in the sample space
NOTE:
1.
0 ≤ 𝑃(𝐸) ≤ 1 (𝑜𝑟 100%)
2.
𝑃(𝑖𝑚𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑒𝑣𝑒𝑛𝑡) =
3.
𝑃(𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑒𝑣𝑒𝑛𝑡) =
4.
𝐴’ is the complement of 𝐴 which means “everything in the sample space
NOT in A”
S
S
A
5.
A’
𝑃(𝐴) + 𝑃(𝐴’) = 1
Can be rearranged into two other forms:
OR
EXAMPLE ① Determine the following probabilities:
a)
rolling a 5 with 1 die;
b)
NOT rolling a 5 with 1 die.
EXAMPLE ② Determine the following probabilities:
a)
tossing 2 heads with 2 coins;
b)
two identical tosses with 2 coins.
EXAMPLE ③ Determine the following probabilities when drawing a card from a standard 52 card deck:
a)
the card is red;
b)
c)
the card is NOT a heart.
the card is a heart;
EXAMPLE ④ Complete the chart for the sum of 2 die.
1
2
3
4
5
6
Determine the following probabilities:
a)
rolling a sum of 8 with 2 dice;
1
2
b)
rolling at least one 3 with 2 dice;
c)
rolling a composite number with 1 die;
d)
rolling a sum that is a prime number with 2
dice.
3
4
5
6
EXAMPLE ⑤ A restaurant owner records the frequency of customer visits in a given month. The results are
recorded in the following table:
Number of Visits
1
2
3
4 or more
a)
Number of Customers
4
6
7
3
Determine the probability that a customer ate at the restaurant:
i)
exactly 3 times;
ii)
fewer than 3 times
b)
If 50 customers visited the restaurant during the next month, determine the number of
customers that would be expected to eat there exactly 2 times.
USING A TREE DIAGRAM TO CALCULATE PROBABILITY
EXAMPLE ⑥ a) Illustrate the possible outcomes of tossing 3 coins using a tree diagram.
b) Determine the following probabilities from the tree diagram:
i)
P(three heads) =
iii)
P(first toss being a tail) =
ii)
P(two tails) =
c) What is the assumption made in the calculations above?
ODDS
𝑂𝐷𝐷𝑆 𝐼𝑁 𝐹𝐴𝑉𝑂𝑅 𝑂𝐹 𝐴 = 𝑃(𝐴): 𝑃(𝐴′ )


𝑂𝐷𝐷𝑆 𝐴𝐺𝐴𝐼𝑁𝑆𝑇 𝐴 = 𝑃(𝐴′): 𝑃(𝐴)
Used in sports to make predictions about a team’s chances for winning
Often predictions involve subjective probability determined by a sports analyst
EXAMPLE ⑦ The probability of the leafs making the playoffs for the 2014-2015 season is 25%. What are the
odds in favor and odds against the leafs making the playoffs?