12.Probability Flashcards
What is a random experiment?
A random experiment is a process or event that has uncertain outcomes, and the outcome cannot be predicted with certainty.
What is the probability of an event?
The probability of an event is a numerical measure that represents the likelihood of that event occurring. It is expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.
What are the odds in favor of an event?
The odds in favor of an event are the ratio of the probability of the event occurring to the probability of the event not occurring. They can be expressed as a fraction, decimal, or ratio.
What are the odds against an event?
The odds against an event are the ratio of the probability of the event not occurring to the probability of the event occurring. They can also be expressed as a fraction, decimal, or ratio.
How are the odds and probability related?
The odds and probability are mathematically related. The probability of an event occurring is equal to the odds in favor of the event divided by the sum of the odds in favor and against the event.
Can the probability of an event be greater than 1 or less than 0?
No, the probability of an event cannot be greater than 1 or less than 0. It always falls within the range of 0 to 1.
How can probability be represented?
Probability can be represented as a fraction, decimal, percentage, or as odds.
What is the relationship between odds and probability?
The relationship between odds and probability can be expressed as: Probability = Odds in Favor / (Odds in Favor + Odds against)
How can odds be calculated from probability?
Odds can be calculated from probability using the formulas: Odds in Favor = Probability / (1 - Probability) and Odds against = (1 - Probability) / Probability.
P (Not A)
1 – P(A)
Probability of an event
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
/ 𝑆𝑎𝑚𝑝𝑙𝑒 𝑠𝑝𝑎𝑐𝑒 𝑜𝑟 𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
Odds in favour of event
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
/ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑛𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒�
Odds against an event
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑢𝑛𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
/ 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑎𝑣𝑜𝑢𝑟𝑎𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
