Simply Probability
On a fair six-sided die, what is the probability you would roll a 5?
1/6
You roll a fair six-sided die twice. The first roll shows a five and the second roll shows a six. What's the probability?
1/6 * 1/6 = 1/36
A box contains 5 purple marbles, 3 green marbles, and 2 orange marbles. Two consecutive draws are made from the box without replacement of the first draw. Find the probability of each event.
P(orange first, green second)
2/10 * 3/9 = 6/90
A diagram shaped like a tree used to display sample space by using one branch for each possible outcome in a probability exercise.
Tree diagram
You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die shows a one
Is this event Independent or Dependent?
Independent
You roll a fair six-sided number cube. What is the probability you roll a number less than 3?
2/6 or 1/3
You toss a fair-sided coin AND then toss a fair-sided die. What is the probability you toss heads and a 3?
1/2 * 1/6 = 1/12
A box contains 5 purple marbles, 3, green marbles, and 2 orange marbles. Two consecutive draws are made from the box without replacement of the first draw. Find the probability of each event.
P(both marbles are purple)
5/10 * 4/9 = 20/90
When given 2 events, the first event does not affect the second event.
Independent Event
A bag contains eight red marbles and four blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag. The first marble is red and the second marble is blue.
Is the event Independent or Dependent?
Dependent
A jar contains 5 purple, 7 red, and 3 yellow marbles. What is the probability that you would NOT draw a purple marble?
10/15 or 2/3
You toss a fair-sided coin AND then toss a fair-sided die. What is the probability you toss heads and an odd number?
1/2 * 3/6 = 3/12 or 1/4
A box contains 5 purple marbles, 3, green marbles, and 2 orange marbles. Two consecutive draws are made from the box without replacement of the first draw. Find the probability of each event.
P( the first marble is purple, and the second is ANY color EXCEPT purple)
5/10 * 5/9 = 25/90
When given 2 events, the first event does affect the second event.
Dependent Event
What are the possible combinations you could have with 14 socks, 11 hats, 5 pairs of pants, and 8 pairs of sunglasses?
6160 combinations
What is the probability of rolling an even number when a fair die is rolled once?
3/6 or 1/2
You toss a fair-sided coin TWO times AND then toss a fair-sided die. What is the probability that you toss heads, tails, and NOT a 3?
1/2 * 1/2* 5/6 = 5/24
If you draw two cards from a standard deck of 52 cards without replacement, find:
P(King first, Jack second)
4/52 * 4/51 = 16/2652
The ratio of the number of outcomes favorable for the event to the total number of possible outcomes
Simple Probability
Ben has 7 shirts and 3 pairs of pants. How many different outfits can Ben have?
21 outfits
What is the probability that a card drawn at random from a deck of cards will be an ace ?
4/52 or 1/13
Bag A contains 9 red marbles and 3 green marbles. Bag B contains 9 black marbles and 6 orange marbles. Find the probability of selecting one green marble from bag A and one black marble from bag B.
3/12 * 9/15 = 27/180
If you draw two cards from a standard deck of 52 cards without replacement, find:
P(2 aces)
4/52 * 3/51 = 12/2652
A way to figure out the number of outcomes in a probability problem by multiplying
Counting Principle
In a hat, there are 4 blue, 5 green, and 3 red marbles. You pick 4 marbles from the hat AND PUT THEM BACK each time. What is the probability that you will pull 4 blue marbles in a row?
4/12 * 4/12 * 4/12 * 4/12 = 256/ 20736 or 1/81