Let S be the Sample space and let F

Event F _{1} , F_{2}……F_{n} |
They are called hypothesis |

P(F _{1}) …… P(F_{2}) |
These probabilities are called priori probabilities as they exist before we obtain any information from experiment |

P( E/F _{1}) ……. P(E/F_{n}) |
These probabilities are called likelihood probabilities as they tell us how event A under consideration occurs |

P(F _{1}/E) …. P(F_{n}/E) |
These probabilities are called the posterior probabilities as they are determined after the result of the experiment is known |

Examples:

**Question**

Of all the smokers in a particular district in India 40% prefer brand X and 60% prefer brand Y. Of those smokers who prefer brand X, 30% are females, and of those who prefer brand Y, 40% are female. What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?

**Solution**

Let F_{1} = "prefer brand A",

F_{2} = "prefer brand B" and

E is the event "female".

We need to find out P(F_{1}|E)

Now from Bayes formula

In this particular situation

So

Or

P(F_{1}|E) =1/3

Of all the smokers in a particular district in India 40% prefer brand X and 60% prefer brand Y. Of those smokers who prefer brand X, 30% are females, and of those who prefer brand Y, 40% are female. What is the probability that a randomly selected smoker prefers brand A, given that the person selected is a female?

Let F

F

E is the event "female".

We need to find out P(F

Now from Bayes formula

In this particular situation

So

Or

P(F

Class 12 Maths Class 12 Physics Class 12 Chemistry Class 12 Biology

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