5 coins are put in a bag. 3 of the coins are weighted with the probability of flipping heads being three times as great than the probability of flipping tails; the remaining coins are fair. One of these coins is selected at random and then flipped once. What is the probability that a weighted coin was selected given that heads was flipped?
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.
Assume,
- W be the event that happens when the selected coin is weighted.
- F be the event that happens when the selected coin is fair.
- H be the event that happens when flipping of coin results in heads.
- T be the event that happens when flipping of coin results in tails.
The required probability is conditional probability that the selected coin is weighted coin given that the flipping of coin results in heads. It can be given as, .
By using the Bayes theorem, can be given as, .
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