Warm-Up remember? 𝑃 𝐸 = 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙 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. Based on your results, predict how many times it would land on heads if you flipped it 100 times. Write and solve a proportion Cross multiply. Divide both sides by 20 to solve for n.

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. Roll a number cube twice Draw a card from a deck of cards, replace it, and draw another card. Take a piece of candy from a jar, eat it, take another piece. Independent 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.

Examples You roll a number cube and spin the spinner. Find each probability: P(5 and A) P(composite and B) A B C

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. P(2 and 3) After drawing one card, you have one less card and only one of them is the number 3. 1 out of 10 cards is the number 2.

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: P(watermelon then cherry) P(strawberry then green apple) P(two green apple)

Probability and geometry 𝑃 𝐸 = 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑇𝑜𝑡𝑎𝑙 Decide how many things or how much space covers everything (Denominator). Decide what we are trying to get (numerator). 6in What is the probability of hitting the shaded region with a dart? 2in 6in 𝑃 𝑦𝑒𝑙𝑙𝑜𝑤 = (2∙2) 6∙6 = 4 36 = 1 9