A branch of mathematics that deals with the happening of a random event is termed probability. It is used in Maths to predict how likely events are to happen. The probability of any event can only be between 0 and 1 and it can also be written in the form of a percentage.
If we are not sure about the outcome of an event, we take help of the probabilities of certain outcomes—how likely they occur. For a proper understanding of probability we take an example as tossing a coin: There will be two possible outcomes—heads or tails. The probability of getting heads is half. You might already know that the probability is half/half or 50% as the event is an equally likely event and is complementary so the possibility of getting heads or tails is 50%. Formula of Probability
Some Terms of Probability Theory
Some Probability FormulasAddition rule: Union of two events, say A and B, then
Complementary rule: If there are two possible events of an experiment so the probability of one event will be the Complement of another event. For example – if A and B are two possible events, then
Conditional rule: When the probability of an event is given and the second is required for which first is given, then
Multiplication rule: Intersection of two other events i.e. events A and B need to occur simultaneously. Then
Solution:
Similar QuestionsQuestion 1: What are the chances of flipping 8 heads in a row? Solution:
Question 2: What are the chances of flipping 13 tails in a row? Solution:
Question 3: What is the probability of flipping a coin 14 times and getting 14 heads? Solution:
Question 4: What are the chances of flipping 25 heads in a row? Solution:
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Here is some code in R to get the answer using the transition matrix method a=c(0.5,0.5,0.5,0.5,0.5,0.5,0.5,0) b=c(0.5,0,0,0,0,0,0,0) c=c(0,0.5,0,0,0,0,0,0) d=c(0,0,0.5,0,0,0,0,0) e=c(0,0,0,0.5,0,0,0,0) f=c(0,0,0,0,0.5,0,0,0) g=c(0,0,0,0,0,0.5,0,0) h=c(0,0,0,0,0,0,0.5,1) M=rbind(a,b,c,d,e,f,g,h) library(expm) Mn<-M%^%150 Mn[1,8] |