if you roll a number cube, calculate the theoretical probability: 1. p(even) 2. p(factor of 6) 3....

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