A group of people is asked to rate a new movie. The results are the following.<?

Question

A group of people is asked to rate a new movie.  The results are the following.<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

                                    Excellent      Good      Fair      Poor

Male                            120                80         60          50

Female                        150                100        40           10

If a person is selected at random, find the following.

Probability of an excellent rating:

Probability of an excellent rating given the person is a female:

Probability of a good rating and the person is a male:

Probability of a fair rating or the person is a female:

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Explanation / Answer

here the formula of probability = number of favourable cases/ total number of cases

so in first case we have to find the probabiltiy of excellent

here excellent male are 120 and female 150 so total favourable is 270 and total number of cases is sum of all males and females

Probability of an excellent rating: 270/610 = 0.4426

now in second excellent and female which is 150 so

Probability of an excellent rating given the person is a female: =150/610= 0.2459

similarly good and male

Probability of a good rating and the person is a male:= 80/610 = 0.1311

similarly fair and female

Probability of a fair rating or the person is a female: = 40/610 = 0.0655

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