Watch the video for a few quick examples of how to find the Probability of A and B / A or B: Probability of A or B (also A and B) Can’t see the video? Click here. You may want to read this article first: Dependent or Independent Event? How to Tell the Difference.
1. What is the Probability of A and B? (adsbygoogle = window.adsbygoogle || []).push({});The probability of A and B means that we want to know the probability of two events happening at the same time. There’s a couple of different formulas, depending on if you have dependent events or independent events.
If the probability of one event doesn’t affect the other, you have an independent event. All you do is multiply the probability of one by the probability of another. ExamplesExample 1: The odds of you getting promoted this year are 1/4. The odds of you being audited by the IRS are about 1 in 118. What are the odds that you get promoted and you get audited by the IRS? Solution: Example 2: The odds of it raining today is 40%; the odds of you getting a hole in one in golf are 0.08%. What are your odds of it raining and you getting a hole in one? Solution:
The formula is a little more complicated if your events are dependent, that is if the probability of one event effects another. In order to figure these probabilities out, you must find p(B|A), which is the conditional probability for the event. Example question: You have 52 candidates for a committee. Four are persons aged 18 to 21. If you randomly select one person, and then (without replacing the first person’s name), randomly select a second person, what is the probability both people will be between 18 and 21 years old? Solution: Step 2: Figure out p(B|A), which is the probability of the next event (choosing a second person aged 18 to 21) given that the first event in Step 1 has already happened. Step 3: Multiply your probabilities from Step 1(p(A)) and Step 2(p(B|A)) together: Your odds of choosing two people aged 18 to 21 are 1 out of 221. 2. What is the Probability of A or B?The probability of A or B depends on if you have mutually exclusive events (ones that cannot happen at the same time) or not. If two events A and B are mutually exclusive, the events are called disjoint events. The probability of two disjoint events A or B happening is:
Example question: What is the probability of choosing one card from a standard deck
and getting either a Queen of Hearts or Ace of Hearts? Since you can’t get both cards with one draw, add the probabilities: If the events A and B are not mutually exclusive, the probability is:
Example question: What is the probability that a card chosen from a standard deck will be
a Jack or a heart?
So: ReferencesSalkind, N. (2019). Statistics for People Who (Think They) Hate Statistics 7th Edition. SAGE. ---------------------------------------------------------------------------
Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free! Comments? Need to post a correction? Please Contact Us. What Makes A and B independent events?Events A and B are independent if: knowing whether A occured does not change the probability of B. Mathematically, can say in two equivalent ways: P(B|A) = P(B) P(A and B)
What are 2 examples of independent events?Here are some INDEPENDENT events:. You flip a coin and get a head and you flip a second coin and get a tail. The two coins don't influence each other.. The probability of rain today and the probability of my garbage being collected today; The garbage will be collected, rain or shine.. Is A and B are two independent events then?If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1- P(A') P(B'). If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1- P(A') P(B').
What is the probability of a ∩ B?We apply P(A ∩ B) formula to calculate the probability of two independent events A and B occurring together. It is given as, P(A∩B) = P(A) × P(B), where, P(A) is Probability of an event “A” and P(B) = Probability of an event “B”.
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