Probability with a Deck of Cards
Probability of pulling a (2)= ?
Hint: There are 52 cards in a deck with four of each number because there are four suits (diamonds, hearts, clubs, and spades)
1/13 or 19%
What is the probability of rolling snake eyes?
(two one's)
1/36 or 3%
What does Union "mean"
Or
Given a 4 color spinner with equal parts (red, blue, yellow, green) what is the probability of spinning red?
1/4 or 25%
Permutation:
How many ways can you arrange the letters in the word CAT?
6!
Key word: arrange
Probability to pull the Queen of Hearts?
1/52 or 2%
P(an even number or a 1)
2/3 or 67%
What does it mean for events to be "independent"?
Independent events in probability are occurrences where the outcome of one event does not affect, influence, or change the probability of another event occurring
Given a 4 color spinner with equal parts (red, blue, yellow, green) what is the probability of spinning purple?
0
CombinationL
How many ways can you choose 2 students from a group of 5?
10
Probability of pulling a 4 OR a 7?
2/13 or 15%
DAILY DOUBLE
What is the probability of rolling a 3, 5, or 0?
1/3 or 33%
When do I use the Multiplication Rule?
When I see "and" or "both"
You have a bag of marbles, four red and five green. What is the probability of choosing red?
(4/9) or 44%
How many ways can 4 runners finish 1st, 2nd, and 3rd?
Permutation!
24
Suppose I pull two cards. What is the probability I pull 2 Jacks?
1/221 or .45%
Suppose you have two dice. What is the probability of rolling a six and a number less than 3?
1/9 aka 0.111
What does Mutually Exclusive Events mean? Give an example.
Events that cannot happen at the same time. Example: Having a peanut allergy and not having a peanut allergy.
Given a 4 color spinner with equal parts (red, blue, yellow, green) what is the probability of spinning red then blue?
1/16 or 6%
How many ways can you choose 3 toppings from 6 options?
Combination! 20
Probability of drawing a card with a 2,3 or 4 on it?
3/13 or 23%
What is the probability of rolling a number that is NOT two?
5/6 aka 0.833
Mutually Exclusive or Non-mutually Exclusive?
Having brown hair and liking tomatoes
Non-mutually exclusive! These two things can happen at the same time.
Suppose I am flipping a coin. What is the probability I flip 3 heads in a row?
.5 x .5 x .5 = 12.5%
Which is larger: the number of ways to choose 2 students from 10, or the number of ways to choose 6 students from 10?
Choosing 6 students from 10 is larger, with 210 ways compared to only 45 ways to choose 2 student
Suppose you draw 4 cards. What is the probability of pulling 2 kings and 2 sevens?
\(\frac{36}{270,725}\)
which is approximately 0.000133 or 0.0133%
Suppose I roll a die three times. What is the probability I roll a 5 each time?
1/216 aka 0.00462
DAILY DOUBLE
Describe the difference between permutations & combinations. Pick one and give an example.
The primary difference between permutations and combinations is that permutations care about the order of selection, while combinations do not. Permutations are for arranging items in a specific sequence (lists, rankings), whereas combinations are for selecting a group (sets, committees) where the order doesn't change the outcome
Suppose I am rolling a die and then randomly selecting a card from a deck of 52. What is the probability of rolling a one THEN picking a red card out of a deck of cards?
1/12 or 8%
1/6 * 1/2 (half of cards are red so 1/2)
Without calculating, determine which is larger: 5P3 or 5C3. Explain your reasoning.
5P3 is larger than 5C3
Here is the simple reasoning: