Types of Events
You pick a marble, replace it, and pick another. Are these events independent or dependent?
Independent
Define "theoretical probability."
Probability based on known possible outcomes. (P = favorable outcomes ÷ total outcomes)
What does each branch in a tree diagram represent?
an outcome or event
You pick a card from a deck. What is the probability of picking a Queen or a King?
(4+4)/52 = 8/52 = 2/13
A bag has 2 green and 5 yellow candies. You pick one, do not replace it, and pick another. What's the probability both are green?
(2/7) × (1/6) = 2/42 = 1/21
Decimal: 0.048 (rounded)
Percent 4.8%
Define "experimental probability."
Probability based on actual experiments or trials. (P = # of times event happens ÷ total trials)
Draw a simple tree diagram for flipping a coin twice. How many outcomes are there?
4 outcomes: HH, HT, TH, TT
You roll two dice. What is the probability that the sum is 7?
6/36 = 1/6 (Outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1))
You spin two spinners, each numbered 1–4. What is the probability that both spinners land on 2?
(1/4) × (1/4) = 1/16
Decimal: 0.0625
Percent 6.25%
You roll a die 50 times and get "2" twelve times. What is the experimental probability of rolling a 2?
12/50 = 6/25 = 0.24 or 24%
A bag has 2 red balls and 1 blue ball. You pick one ball, don't replace it, and pick another. How many total outcomes are there in the tree diagram?
Draw the diagram
6 outcomes
A spinner has 1, 2, 3, and 4. If you spin twice, what is the probability the sum is 5?
4/16 = 1/4 (Outcomes: (1,4), (2,3), (3,2), (4,1))
If you draw 2 cards from a deck without replacement, what is the probability that both cards are Kings?
(4/52) × (3/51) = 12/2652 = 1/221
Decimal: 0.0045
Percent: 0.45%
The theoretical probability of spinning red is 1/4. After 100 spins, you get red 10 times. Is your result experimental or theoretical?
Experimental
Create a tree diagram for rolling a die and flipping a coin. What are all the possible outcomes?
Draw the tree
12 outcomes: (1,H), (1,T), (2,H), (2,T), (3,H), (3,T), etc.
You roll a die and flip a coin. Find the probability of rolling an even number and flipping tails.
(3/6) × (1/2) = 3/12 = 1/4
0.25
25%
A bag has 5 red and 3 blue marbles. You pick one, replace it, and pick another. Find the probability of picking a blue then a red.
(3/8) × (5/8) = 15/64
0.23
23%
Explain one reason why experimental probability might be different from theoretical probability.
Random variation or chance affects real trials.
You spin a spinner (red, blue) and then pick a marble (green, yellow, orange). List all outcomes.
Red-Green, Red-Yellow, Red-Orange, Blue-Green, Blue-Yellow, Blue-Orange (6 outcomes)
A classroom has 10 boys and 15 girls. If two students are picked without replacement, what is the probability both are girls?
(15/25) × (14/24) = (3/5) × (7/12) = 21/60 = 7/20
0.35
35%