Question Video: Calculating Probabilities Using a Two-Way Table Mathematics

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

We want to find the probability that a new alien species chosen at random was encountered by starship Geoda. This doesn’t specify which season we’re interested in, so we’re going to use the total. And so we begin by recalling that the probability of an event occurring is found by dividing the number of ways that event can occur by the total number of possible outcomes. So in this case, we’re going to find the number of alien species found in total by starship Geoda. And then we’ll divide that by the total number of alien species encountered altogether.

Looking at the totals, we see that starship Geoda discovered a total of 72 alien species. And the total was 83. So the probability that a new alien species chosen at random was encountered by starship Geoda is found by dividing 72 by 83, which is 0.8674 and so on. Correct to three decimal places, that’s 0.867.

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