Percent Of All Liquid C Exercise 5

value368 Pointsexercise 5 91nineteen Percent Of All Liquid Crystal

Determine the probability that in a collection of three independent LCD purchases, at least one is a Samsung, given that nineteen percent of all liquid crystal displays (LCDs) are manufactured by Samsung. Round your answer to three decimal places.

In this problem, the key data is that 19% (or 0.19) of LCDs are made by Samsung. The complement event—none of the three LCDs purchased are Samsung—is more straightforward to compute first. The probability that a single LCD is not Samsung is 1 - 0.19 = 0.81. Since the purchases are independent, the probability that all three are not Samsung is (0.81)^3.

Calculating, (0.81)^3 = 0.531441.

Therefore, the probability that at least one of the three LCDs is Samsung is 1 minus the probability that none are Samsung: 1 - 0.531441 = 0.468559.

Rounding to three decimal places yields 0.469.

Paper For Above instruction

The probability that in a selection of three independent LCD purchases at least one is a Samsung can be determined utilizing the concept of complementary probability. Given that 19% of all LCDs are manufactured by Samsung, the probability that a randomly selected LCD is not Samsung is 0.81. Since each purchase is independent, the probability that none of the three LCDs are Samsung is (0.81)^3, which equals approximately 0.531441. To find the probability that at least one is Samsung, subtract this from 1, yielding 1 - 0.531441 = 0.468559. Rounded to three decimal places, the probability is approximately 0.469. This approach illustrates the application of the complement rule in probability, which simplifies calculations involving at least one occurrence of a specific event.

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