Video: US-SAT04S4-Q09-295182735746

The given table shows the number of televisions produced daily by a factory. The factory produces televisions in two resolutions, HD 1080 and ultra-HD 4K. For each resolution, the factory produces the televisions in two sizes: 43 inches and 55 inches. If a television is randomly selected from the televisions produced on a day, which of the following is the closest to the probability that the resolution of the selected TV is ultra HD 4K and its size is 55 inches? [A] 0.79 [B] 0.441 [C] 0.345 [D] 0.156

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Video Transcript

The given table shows the number of televisions produced daily by a factory. The factory produces televisions in two resolutions, HD 1080 and ultra-HD four K. For each resolution, the factory produces the televisions in two sizes, 43 inches and 55 inches. If a television is randomly selected from the televisions produced on a day, which of the following is the closest to the probability that the resolution of the selected TV is ultra HD [four] K and its size is 55 inches? A) 0.79. B) 0.441. C) 0.345. Or D) 0.156.

We know that the probability of a certain outcome is the number of favorable outcomes over all possible outcomes. Our desired outcome is choosing a TV that is ultra HD four K and 55 inches. On our table, we need to look for the intersection of the ultra HD four K row and the 55 inches column. The intersection is 413. This tells us that, on any given day, 413 TVs are produced that have 55 inches and ultra HD four K. If we’re going to select a random TV made on a day, then 413 of them will fit the criteria.

But what should the denominator be? The denominator should be all possible outcomes. To find this, we look for the intersection of the total row and the total column. Every day, this factory produces 2652 TVs. And that means the random selection will be out of 2652. We need to divide 413 by 2652.

When we do this, we get 0.1557315 continuing. We want to round this to three decimal places, as most of our answer choices are also rounded to three decimal places. To the right of the third decimal place, in the fourth decimal place, there’s a seven. And that means we need to round up to 0.156. 413 out of 2652 is about 0.156, which is option D.

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