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70% of a certain species of tomato live after transplanting from pot to garden. najib transplants 3 of these tomato plants. assume that the plants live independently of each other. let x = the number of tomato plants that live. what is the probability that exactly 2 of the 3 tomato plants live? you may round your answer to the nearest hundredth.

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Final answer:

To calculate the probability that exactly 2 out of 3 tomato plants live after transplanting, with a survival rate of 70%, we use the binomial probability formula. The calculation gives us a probability of approximately 0.44 or 44% when rounded to the nearest hundredth.

Step-by-step explanation:

The question asks us to calculate the probability that exactly 2 out of 3 tomato plants will survive after being transplanted, given that the survival rate for each plant is 70%. To find this probability, we can use the binomial probability formula, which is P(X = k) = nCk * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, p is the probability of success on a single trial, and nCk is the number of combinations.

For this problem:

  • n = 3 (the number of plants)
  • k = 2 (we want exactly 2 plants to live)
  • p = 0.7 (the probability of any one plant living)

The number of combinations of n things taken k at a time is given by the binomial coefficient, calculated as nCk. Thus, we have 3C2 = 3.

The probability calculation is:

P(X = 2) = 3C2 * 0.7^2 * (1-0.7)^(3-2) = 3 * 0.49 * 0.3 ≈ 0.441

So, the probability that exactly 2 of the 3 tomato plants will live after transplanting is approximately 0.44 or 44% when rounded to the nearest hundredth.

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