Single Pick Probability AND vs. OR Sequential Probability With Replacement Conditional Disjoint vs. Non Disjoint Unit 4 – Probability – Part 1

Single Pick

Unit 4 – Probability – Part 1 Single Pick AND Ex: What is the probability of selecting a face card that’s also a heart from a deck of 52 cards?

Unit 4 – Probability – Part 1 Single Pick AND Ex: What is the probability of selecting a face card that’s also a heart from a deck of 52 cards? P(A) = Probability(Face Card) P(B) = Probability(Heart) P(A∩ B) = Probability(Face Card and Heart) P(A∩ B) = 3/52 Concept Check: What is the probability of rolling a prime number that’s also less than 10 on a 20 sided dice?

Unit 4 – Probability – Part 1 Single Pick AND OR Ex: What is the probability of selecting a face card that’s also a heart from a deck of 52 cards? P(A∩ B) = 3/52 Ex. What is the probability of selecting a 7 or a heart from a deck of 52 cards? P(A ∪ B) = 16/52 Concept Check: What is the probability of rolling either an even number or a prime number on a 14 sided dice?

Unit 4 – Probability – Part 1 Single Pick Sequential AND With Replacement OR Ex: What is the probability of selecting a face card that’s also a heart from a deck of 52 cards? P(A∩ B) = 3/52 Ex. What is the probability of selecting a 7 or a heart from a deck of 52 cards? P(A ∪ B) = 16/52 Ex. What is the probability of rolling a 6 on a single dice, twice in a row? (1/6)(1/6) = 1/36 Concept Check: What is the probability of beating your friend twice at chess if you have a known 80% win rate?

Unit 4 – Probability – Part 1 Single Pick Sequential AND Without Replacement With Replacement OR Ex: What is the probability of selecting a face card that’s also a heart from a deck of 52 cards? P(A∩ B) = 3/52 Ex. What is the probability of selecting a 7 or a heart from a deck of 52 cards? P(A ∪ B) = 16/52 Ex. What is the probability of rolling a 6 on a single dice, twice in a row? (1/6)(1/6) = 1/36 Ex. What is the probability of getting a pair of Aces when drawing the top 2 cards of a regular deck of cards? (4/52)(3/51) = 12/2652 Concept Check: What is the probability of randomly selecting 4 spades from a standard deck of cards?

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Disjoint Example: What is the probability of selecting an Ace and a King in a single pick from a normal deck of cards? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment.

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Disjoint Example: What is the probability of selecting an Ace and a King in a single pick from a normal deck of cards? The events “Ace” and “King” are disjoint, meaning they do not overlap. In this case, we had an “and” scenario which means it is impossible. Because the two events are non overlapping, both cannot occur at the same time. P(A∩ B) = 0/52 = Note: Both disjoint and non disjoint automatically imply you are in a single pick environment.

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Disjoint Example: What is the probability of selecting an Ace or a King in a single pick from a normal deck of cards? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment.

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Disjoint Example: What is the probability of selecting an Ace or a King in a single pick from a normal deck of cards? The events “Ace” and “King” are disjoint, meaning they do not overlap. In this case, we have an “or” scenario which means either is acceptable. Because the two events are non overlapping, we simply add. P(A ∪ B) = P(A) + P(B) = 8/52 Note: Both disjoint and non disjoint automatically imply you are in a single pick environment.

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Non Disjoint Example: What is the probability of selecting a Face card and a Heart in a single pick from a normal deck? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment.

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Non Disjoint Example: What is the probability of selecting a Face card and a Heart in a single pick from a normal deck? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment. The events “Face Card” and “Heart” are non disjoint, meaning they overlap. In this case, we had an “and” scenario which means both conditions must be satisfied. P(A∩ B) = 3/52

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Non Disjoint Example: What is the probability of selecting a Face card or a Heart in a single pick from a normal deck? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment.

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Non Disjoint Example: What is the probability of selecting a Face card or a Heart in a single pick from a normal deck? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment. The events “Face Card” and “Heart” are non disjoint, meaning they overlap. In this case, we had an “or” scenario which means either condition can be true. P(A ∪ B) = 22/52

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Non Disjoint Example: What is the probability of selecting a Face card or a Heart in a single pick from a normal deck? Note: Both disjoint and non disjoint automatically imply you are in a single pick environment. P(A ∪ B) = 22/52 P(A ∪ B) = P(A) + P(B) – P(A∩ B) P(A ∪ B) = 12/ /52 – 3/52 P(A ∪ B) = 22/52

Unit 4 – Probability – Part 1 Disjoint vs. Non Disjoint Concept Check part 1: Say if the events are disjoint or non disjoint - Aces and Hearts - Even numbers and primes - Spades and 7s - Juniors and Seniors - Teenagers and people with drivers licenses

Discrete Probability Continuous Probability Binomial Distributions Geometric Distributions Unit 4 – Probability – Part 2