You have two biased coins. Coin A comes up heads with probability 0.4. Coin B comesup heads with probability 0.7. However, you are not sure which is which so you choose a coin randomly and you flip it. If the flip is heads, you guess that the flipped coin is B; otherwise,you guess that the flipped coin is A. Let events A and B designate which coin was picked. What is the probability P[C] that your guess is correct?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
You have two biased coins. Coin A comes up heads with
randomly and you flip it. If the flip is heads, you guess that the flipped coin is B; otherwise,you guess that the flipped coin is A. Let
What is the probability P[C] that your guess is correct?
The probability of getting a coin A=
The probability of getting a coin B=
Let us denote H=head and T=tail
Given that coin A comes up heads with a probability of 0.4. Coin B comes up heads with a probability of 0.7.
P(H|A)=0.4
P(H|B)=0.7
So, P(T|A)=1-0.4=0.6
And P(T|B)=1-0.7=0.3
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