General Probability Rules (30 sec)
Given an event, A, what equation gives you the probability that event A will NOT occur?
What is ....
P(Ac) = 1 - P(A)
or
P(Ac)+P(A)=1
Find the probability of rolling a fair die three times and getting three fours.
What is ...
P(rolling three 4s) = P(4)*P(4)*P(4) = P(4)^3
or (1/6)*(1/6)*(1/6)= (1/6)^3 = 1/216
Events that do not impact each other's probability.
What is...
independent
A coin is tossed 3 times. What is the probability that it lands on heads exactly one time?
What is...
0.375
What year was KPS founded?
1894
Given two independent events, A and B, what is the probability that event A and B occurs.
What is...
P(A and B) = P(A) * P(B)
The rule for the probability of pulling a red or queen from a standard deck of cards.
What is...
P(Red or Queen)= P(red)+P(queen) - P(red and queen)
= 39/52 + 4/52 - 2/52 = 41/52
Two events that cannot occur simultaneously
What is....
mutually exclusive or disjoint
Is rolling two dice where at least one of them is a 4 and the sum is 7 independent events? Justify your answer.
No, they are not independent
P(sum of 7) = 6/36 = 1/6
P(sum of 7 GIVEN one die is 4) = 2/11
They are not equal probabilities, therefore the events are NOT independent
How many teachers are in the upper school math department?
Given two mutually exclusive events, A and B, what is the probability that event A or event B occurs?
What is ...
P(A or B)= P(A) + P(B)
The two equations used to determine independence between 2 events.
What is...
P(A|B)=P(A)
or
P(B|A)=P(B)
Interpret the following:
P(A U B) and P(C | D)
What is...
the probability of A or B and C given D?
What is the probability of being dealt 5 cards that are a royal flush?
(A royal flush is when you have 10, J, Q, K, and A all of the same suit).
You may leave your answer as a fraction.
P(royal flush) =
4* (5/52)(4/52)(3/52)(2/52)(1/52)
Ms. Majumder relocated to the United States in December 2022.
Which country did she relocate from?
India
Given two events, A and B, what is the probability that event A and B occurs.
What is...
P(A and B) = P(A) * P(B|A)
You are dealt two cards from a standard 52 card playing deck. What is the conditional probability that the second card is a diamond given that the first is a diamond?
P(diamond | first is a diamond) =
(13/52)*(12/52) = .0577
Two events that do impact each other's probability
what is ...
dependent (or not independent)
90% of the people who have a particular disease will have a positive result on a given diagnostic test (90% accuracy). If 5% of a certain population has the disease, what percent of the population would test positive for the disease?
What is ...
14% or 0.14
What is the name of the dining hall catering service?
What is ...
Meriwether Godsey
Given two events, A and B, what is the probability that event A or event B occurs?
What is ...
P(A or B)= P(A) + P(B) - P(A and B)
or
P(A or B)= P(A) + P(B) - P(A)*P(B|A)
Amanda is a high school softball player. She gets a hit 70% of the time. That means her average is 0.70. What is the probability that she gets her first successful hit on her third swing?
What is ...
0.3*0.3*0.7= 0.063
Set of values that contains all of the possible outcomes
what is...
sample space
Find the probability of 2 or more people from a group of 5 having the same birthday
What is ...
1- P(none have the same birthday)
P(none have the same birthday)= (365/365) *(364/365) * (363/365) * (362/365) * (361/365)
=0.0271
Whichever team is closest to the correct number will win the points. Without going over, how many faculty members are at KPS across ALL divisions?
99