if you roll a number cube, calculate the theoretical probability: 1. p(even) 2. p(factor of 6) 3....
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Warm-Up remember?
If you roll a number cube, calculate the theoretical probability:1. P(even)2. P(factor of 6)3. P(prime)
You rolled a number cube 25 times and recorded the number it landed on. The results are given in the table. Based on the experiment find each probability:4. P(8)
5. P(composite)
Number
Frequency
1
2
3
4
5
6
Making Predictions
How do you make predictions based on probability?
Example:You flipped a coin 20 times. 12 times it landed on heads, 8 on tails.1. Based on your results,
predict how many times it would land on heads if you flipped it 100 times.
Write and solve a proportion
12
20 100
12 100 20
1200 20
20 20
60
n
n
n
n
Divide both sides by 20 to solve for n.
Cross multiply.
Independent Events vs. Dependent Events
What are independent events?
What are dependent events?
When the probability of the second event is NOT affected by the first event.(flipping a coin, drawing a card, replacing it and draw another…)
When the probability of the second event IS affected by the first event.(draw a name, keep it out, and then draw another name)
Examples - Determine if the events are dependent or independent.
1. Roll a number cube twice
2. Draw a card from a deck of cards, replace it, and draw another card.
3. Take a piece of candy from a jar, eat it, take another piece.
1. Independent
2. Independent
3. Dependent
Independent Events
How do you find the probability of independent events?
Example:You roll a number cube twice.1. P(1 and even)
1.
P(A and B) = P(A) P(B)
1 1P(1) = P(even) =
6 2
1 1 1P(1 and even)
6 2 12
Examples
You roll a number cube and spin the spinner. Find each probability:
1. P(5 and A)
2. P(composite and B)
AAB
CBA
1 5 51.
6 8 48
1 1 12.
3 4 12
Dependent Events
How do you calculate the probability of dependent events?
Example:You have cards numbered 0 to 9. You select a card, keep it, select another.1. P(2 and 3)
P(A then B) = P(A) P(B after A)
1 1 1
10 9 90
1 out of 10 cards is the number 2.
After drawing one card, you have one less card and only one of them is the number 3.
A candy jar contains the following candy: 4 strawberry, 5 green apple, 2 watermelon, and 1 cherry. You select a piece, eat it, and select another. Calculate each probability:
1. P(watermelon then cherry)
2. P(strawberry then green apple)
3. P(two green apple)
1 1 11.
6 11 66
1 5 52.
3 11 33
5 4 20 53.
12 11 132 33
Probability and geometry
Decide how many things or how much space covers everything (Denominator).
Decide what we are trying to get (numerator).
6in
6in
2in
What is the probability of hitting the shaded region with a dart?
𝑃 (𝑦𝑒𝑙𝑙𝑜𝑤 )=(2 ∙2)6 ∙6
= 436
=19