Question Video: Calculating a Conditional Probability from a Two-Way Frequency Table

A fanzine website for the TV show A Maze in Space collects data on the number of new alien species encountered by two starships in each season of the show. The data for seasons 1, 2, and 7 are shown in the table below, split between two starships: Zeta and Geoda. Given that a new alien species was encountered in season 7, find the probability that they were encountered by starship Geoda. Give your answer to three decimal places.

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Video Transcript

A fanzine website for the TV show, A Maze in Space, collects data on the number of new alien species encountered by two starships in each season of the show. The data for seasons one, two, and seven are shown in the table below, split between two starships: Zeta and Geoda. Given that a new alien species was encountered in season seven, find the probability that they were encountered by starship Geoda. Give your answer to three decimal places.

The words “given that” implies that we are dealing with conditional probability. The table shows the data for two starships in three seasons: season one, two, and seven. We will now clear some space for our calculations.

We are told that the species was encountered in season seven, which means we are only interested in this column of the table. The total number of species that were encountered in season seven is equal to 13. We need to work out which of these species were encountered by starship Geoda. Five species were encountered by starship Zeta, and eight species were encountered by starship Geoda.

The probability that an alien species was encountered by starship Geoda given that it was encountered in season seven is, therefore, equal to eight over 13 or eight thirteenths. The line in a fraction means divide. And eight divided by 13 is equal to 0.615384 and so on. We want to give our answer to three decimal places. Therefore, the three is the deciding number. As this is less than five, we round down, giving us an answer of 0.615. Given that a new alien species was encountered in season seven, the probability that they were encountered by starship Geoda is 0.615.

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